Modern Physics
E28-1
kg29103.3 m/sec. Its
frequency will be
(1) Hz3103 (2) Hz3106
(3) Hz12105.7 (4) Hz13105.1
Ans. (4)
Sol.h
pc
c
hp
34
829
106.6
103103.3
Hz13105.1
Q.2 The rest mass of the photon is
(1)0
(2) (3) Between 0 and
(4) Equal to that of an electron
Ans. (1)
Q.3 If the momentum of a photon is p, then its frequency is
Where m is the rest mass of the photon
(1)c
ph(2)
h
pc
(3)c
mh(4)
h
mc
Ans. (2)
Sol.h
pc
c
h
c
Ep
Q.4 Which of the following statement is not correct
(1) Photographic plates are sensitive to infrared rays
(2) Photographic plates are sensitive to ultraviolet rays
(3) Infra-red rays are invisible but can cast shadows
like visible light
(4) Infrared photons have more energy than photons
of visible light
Ans. (4)
Sol. ;1
E also visibleinfrared so visibleinfrared EE
Q.5 There are 1n photons of frequency 1 in a beam of
light. In an equally energetic beam, there are 2n
photons of frequency 2 . Then the correct relation is
(1) 12
1 n
n(2)
2
1
2
1
n
n
(3)1
2
2
1
n
n(4) 2
2
21
2
1
n
n
Ans. (3)
Sol.1
2
2
11
n
n
nnhE .
Q.6 Einstein’s photoelectric equation states
that hEk . In this equation kE refers to
(1) Kinetic energy of all the emitted electrons
(2) Mean kinetic energy of the emitted electrons
(3) Maximum kinetic energy of the emitted electrons
(4) Minimum kinetic energy of the emitted electrons
Ans. (3)
Sol. According to Einstein’s photoelectric equation
Q.7 The threshold wavelength for photoelectric emission
from a material is 5200 Å. Photo-electrons will be
emitted when this material is illuminated with
monochromatic radiation from a
(1) 50 watt infrared lamp
(2) 1 watt infrared lamp
(3) 50 watt ultraviolet lamp
(4) Both (3) and (4)
Ans. (4)
Sol. In this case, for photoelectric emission the wavelength
of incident radiations must be less then Å5200 .
Wavelength of ultraviolet radiations is less then this
value (5200 Å) but wavelength of infrared radiations is
higher than this value.
Q.8 Threshold frequency for a metal is 1510 Hz. Light of
Å4000 falls on its surface. Which of the following
statements is correct
(1) No photoelectric emission takes place
(2) Photo-electrons come out with zero speed
(3) Photo-electrons come out with 103 m/sec speed
(4) Photo-electrons come out with 105 m/sec speed
Ans. (1)
Sol. Frequency of light of wavelength )4000( Å is
15
10
8
1075.0104000
103
cwhich is less than
the given threshold frequency. Hence no photoelectric
emisssion takes place.
Q.9 When light falls on a metal surface, the maximum kinetic
energy of the emitted photo-electrons depends upon
(1) The time for which light falls on the metal
(2) Frequency of the incident light
(3) Intensity of the incident light
(4) Velocity of the incident light
Ans. (2)
Modern Physics
Photoelectric effect
Q.1 The momentum of a photon is
EXERCISE-I
Modern Physics
E28-2
Sol. );( 0max WhK frequency of incident light.
Q.10 The work function of a metal is 4.2 eV, its threshold
wavelength will be
(1) 4000 Å (2) 3500 Å
(3) 2955 Å (4) 2500 Å
Ans. (4)
Sol. Intensity (No. of photons) (No. of photoelectrons)
Q.11 The work function of metal is 1 eV. Light of wavelength
3000 Å is incident on this metal surface. The velocity
of emitted photo-electrons will be
(1) 10 m/sec (2) 3101 m/sec
(3) 4101 m/sec (4) 6101 m/sec
Ans. (4)
Sol. eVEKWE 125.43000
12375;max0
eVeVeVWEK 125.31125.40max
Jmv 192max 106.1125.3
2
1
31
19
max101.9
106.1125.32
v sm /101 6
Q.12 The work function of a metal is 19106.1 J. When
the metal surface is illuminated by the light of
wavelength 6400 Å, then the maximum kinetic energy
of emitted photo-electrons will be
(Planck’s constant Jsh 34104.6 )
(1) J191014 (2) J19108.2
(3) J19104.1 (4) eV19104.1
Ans. (3)
Sol.19
10
834
0max 106.1106400
103104.6
W
hcK
J19104.1
Q.13 The work function for metals A, B and C are respectively
1.92 eV, 2.0 eV and 5 eV. According to Einstein’s
equation, the metals which will emit photo electrons
for a radiation of wavelength 4100 Å is/are
(1) None of these (2) A only
(3) A and B only (4) All the three metals
Ans. (3)
Sol. Energy of incident radiations (in eV)
eV01.34100
12375
Work function of metal A and B are less then eV01.3 ,
so A and B will emit photo electrons.
with light of wavelength 332 nm. The retarding potential
required to stop the escape of photo-electrons is
(1) 4.81 eV (2) 3.74 eV
(3) 2.66 eV (4) 1.07 eV
Ans. (3)
Sol. Energy of incident light eVeVE 72.33320
12375)(
)3320332( Ånm
According to the relation 00 eVWE
e
eVeV
e
WEV
07.172.3)( 00
.65.2 Volt
Q.15 The number of photo-electrons emitted per second
from a metal surface increases when
(1) The energy of incident photons increases
(2) The frequency of incident light increases
(3) The wavelength of the incident light increases
(4) The intensity of the incident light increases
Ans.. (4)
Sol. Intensity (No. of photons) (No. of photoelectrons)
Q.16 A photo cell is receiving light from a source placed at
a distance of 1 m. If the same source is to be placed at
a distance of 2 m, then the ejected electron
(1) Moves with one-fourth energy as that of the initial
energy
(2) Moves with one-fourth of momentum as that of
the initial momentum
(3) Will be half in number
(4) Will be one-fourth in number
Ans. (4)
Sol. Number of ejected electrons 2)Distance(
1)(Intensity
Therefore an increment of distance two times will
reduce the number of ejected electrons to th4
1of the
previous one.
Q.17 In a photoelectric experiment for 4000 Å incident
radiation, the potential difference to stop the ejection
is 2 V. If the incident light is changed to 3000 Å, then
the potential required to stop the ejection of electrons
will be
(1) 2 V (2) Less than 2 V
(3) Zero (4) Greater than 2 V
Ans. (4)
Sol. According to Einstein’s photoelectric equation
max0 KWE
00
11
e
hcV
Hence if decreases 0V increases.
Experimental study of photoelectric effect
Q.14 A metal surface of work function 1.07 eV is irradiated
Modern Physics
E28-3
Q.18 Stopping potential for photoelectrons
(1) Does not depend on the frequency of the incident
light
(2) Does not depend upon the nature of the cathode
material
(3) Depends on both the frequency of the incident
light and nature of the cathode material
(4) Depends upon the intensity of the incident light
Ans. (3)
Q.19 Which one of the following is true in photoelectric
emission
(1) Photoelectric current is directly proportional to the
amplitude of light of a given frequency
(2) Photoelectric current is directly proportional to the
intensity of light of a given frequency at moderate
intensities
(3) Above the threshold frequency, the maximum K.E.
of photoelectrons is inversely proportional to the
frequency of incident light
(4) The threshold frequency depends upon the
wavelength of incident light
Ans. (2)
Q.20 If in a photoelectric experiment, the wavelength of
incident radiation is reduced from 6000 Å to 4000 Å
then
(1) Stopping potential will decrease
(2) Stopping potential will increase
(3) Kinetic energy of emitted electrons will decrease
(4) The value of work function will decrease
Ans. (2)
Sol. Stopping potential
00
11
e
hcV . As decreases
so 0V increases.
Q.21 As the intensity of incident light increases
(1) Photoelectric current increases
(2) Photoelectric current decreases
(3) Kinetic energy of emitted photoelectrons increases
(4) Kinetic energy of emitted photoelectrons decreases
Ans. (1)
Sol. Intensity increases means more photons of same energy
will emit more electrons of same energy, hence only
photoelectric current increases.
Q.22 The maximum kinetic energy of photoelectrons emitted
from a surface when photons of energy 6 eV fall on it is
4 eV. The stopping potential in volts is
(1) 2 (2) 4
(3) 6 (4) 10
Ans. (2)
Sol. eVVK s ||max VVs 4||
(1) When it is stationary
(2) When it is in motion with the velocity of light only
(3) When it is in motion with any velocity
(4) None of the above
Ans. (3)
Sol. According to de-Broglie hypothesis.
Q.24 A photon, an electron and a uranium nucleus all have
the same wavelength. The one with the most energy
(1) Is the photon
(2) Is the electron
(3) Is the uranium nucleus
(4) Depends upon the wavelength and the properties
of the particle.
Ans. (1)
Sol. :2mE
h
mv
h
2
2
2 m
hE
is same for all, som
E1
. Hence energy will be
maximum for particle with lesser mass.
Q.25 When the kinetic energy of an electron is increased,
the wavelength of the associated wave will
(1) Increase
(2) Decrease
(3) Wavelength does not depend on the kinetic energy
(4) None of the above
Ans. (2)
Sol.EmE
h
p
h 1;
2 (h and m = constant)
Q.26 If the de-Broglie wavelengths for a proton and for a
particle are equal, then the ratio of their velocities
will be
(1) 4 : 1 (2) 2 : 1 (3) 1 : 2 (4) 1 : 4
Ans. (1)
Sol. 1
4;
1
2
2
1
2211
m
m
v
v
vm
h
vm
h
Q.27 The de-Broglie wavelength associated with an
electron having kinetic energy E is given by the
expression
(1)mE
h
2(2)
mE
h2(3) mhE2 (4)
h
mE22
Ans. (1)
Sol.mE
h
mv
hmEmvEmv
2;2
2
1 2
Q.28 Dual nature of radiation is shown by
(1) Diffraction and reflection
(2) Refraction and diffraction
(3) Photoelectric effect alone
(4) Photoelectric effect and diffraction
De-Broglie Wavelength
Q.23 Wave is associated with matter
Modern Physics
E28-4
Ans. (4)
Sol. natureDualnatureWavenDiffractio
natureParticleeffectricPhotoelect
Q.29 The de-Broglie wavelength of an electron having
eV80 of energy is nearly (1eV = 1.6 10–19 J, Mass of
electron = 9 10–31kg , Plank’s constant = 6.6 10–34 J-
sec)
(1) 140 Å (2) 0.14 Å (3) 14 Å (4) 1.4 Å
Ans. (4)
Sol. 1931
34
106.1801092
106.6
2
mE
h
Å4.1
Q.30 The kinetic energy of electron and proton is J3210 .
Then the relation between their de-Broglie wavelengths
is
(1) ep (2) ep
(3) ep (4) ep 2
Ans. (1)
Sol. By usingmE
h
2 E = 10–32 J = Constant for both
particles. Hencem
1 Since ep mm so .ep
Q.31 The de-Broglie wavelength of a particle accelerated
with 150 volt potential is 1010 m. If it is accelerated by
600 volts p.d., its wavelength will be
(1) 0.25 Å (2) 0.5 Å
(3) 1.5 Å (4) 2 Å
Ans. (2)
Sol. By usingV
1
1
2
2
1
V
V
2
150
60010
2
10
2= 0.5 Å.
Q.32 The de-Broglie wavelength of a neutron at 27oC is .
What will be its wavelength at 927oC
(1) / 2 (2) / 3
(3) / 4 (4) / 9
Ans. (1)
Sol.T
neutron
1
1
2
2
1
T
T
2300
1200
)27273(
)927273(
2
.
22
principal quantum number n > 4, then the total possible
number of elements will be
(1)60 (2)32 (3)4 (4)64
Ans.. (1)
Sol. For n=1, maximum number of states 22 2 n and for
n = 2, 3, 4, maximum number of states would be 8, 18, 32
respectively, Hence number of possible elements
= 2 + 8 + 18 + 32 = 60.
Q.34 In the Bohr’s hydrogen atom model, the radius of the
stationary orbit is directly proportional to (n = principle
quantum number)
(1) 1n (2) n (3) 2n (4) 2n
Ans. (4)
Sol. Bohr radius2
2
220 ; nrZme
hnr
Q.35 In the n th orbit, the energy of an electron
eVn
En 2
6.13 for hydrogen atom. The energy
required to take the electron from first orbit to second
orbit will be
(1) eV2.10 (2) eV1.12
(3) eV6.13 (4) eV4.3
Ans.. (1)
Sol.
1 2E 3.4 (13.6) 10.2eV
Q.36 The Lyman series of hydrogen spectrum lies in the
region
(1) Infrared (2) Visible
(3) Ultraviolet (4) Of X rays
Ans.. (3)
Sol. Lyman series lies in the UV region
Q.37 The size of an atom is of the order of
(1) m810 (2) m1010
(3) m1210 (4) m1410
Ans. (2)
Sol. The size of the atom is of the order of 1Å = 10–10m.
Q.38 Which one of the series of hydrogen spectrum is in
the visible region
(1) Lyman series (2) Balmer series
(3) Paschen series (4) Bracket series
Bohr’s model
Q.33 If in nature there may not be an element for which the
Modern Physics
E28-5
Ans. (2)
Sol. Balmer series lies in the visible region.
Q.39 The energy levels of the hydrogen spectrum is shown
in figure. TherearesometransitionsA, B, C, D and E.
Transition A, B and C respectively represent
(1) First member of Lyman series, third spectral line of
Balmer series and the second spectral line of Paschen
series
(2) Ionization potential of hydrogen, second spectral
line of Balmer series and third spectral line of Paschen
series
(3) Series limit of Lyman series, third spectral line of
Balmer series and second spectral line of Paschen
series
(4) Series limit of Lyman series, second spectral line of
Balmer series and third spectral line of Paschen series
Ans. (3)
Sol. Transition A (n = to 1) : Series limit of Lyman series
Transition B (n = 5 to n = 2) : Third spectral line of
Balmer series
Transition C (n = 5 to n = 3) : Second spectral line of
Paschen series
Q.40 The following diagram indicates the energy levels of a
certain atom when the system moves from 2E level to
E, a photon of wavelength is emitted. The
wavelength of photon produced during its transition
from3
4 Elevel to E is
(1) 3/ (2) 4/3 (3) 3/4 (4) 3
Ans. (4)
Sol.
hcE
hcEE 2
3'3
'
'3'3
4
hcEhcE
E
Q.41 Figure shows the energy levels P, Q, R, S and G of an
atom where G is the ground state. A red line in the
emission spectrum of the atom can be obtained by an
energy level change from Q to S. A blue line can be
obtained by following energy level change
(1) P to Q (2) Q to R
(3) R to S (4) R to G
Ans. (4)
Sol. If E is the energy radiated in transition
then QPRQSRSQGR EEEEE
For getting blue line energy radiated should be
maximum
1E . Hence (4) is the correct option.
Q.42 The figure indicates the energy level diagram of an
atom and the origin of six spectral lines in emission
(e.g. line no. 5 arises from the transition from level B to
A). The following spectral lines will also occur in the
absorption spectrum
1 2 3 4 5 6 X
A
B
C
(1) 1, 4, 6 (2) 4, 5, 6
(3) 1, 2, 3 (4) 1, 2, 3, 4, 5, 6
Ans. (3)
Sol. The absorption lines are obtained when the electron
jumps from ground state (n = 1) to the higher energy
states. Thus only 1, 2 and 3 lines will be obtained.
Q.43 In the lowest energy level of hydrogen atom, the
electron has the angular momentum
(1) h/ (2) /h
(3) 2/h (4) h/2
Ans. (3)
Modern Physics
E28-6
Sol.2
nhmvr , for n =1 it is
2
h
Q.44 The absorption transitions between the first and the
fourth energy states of hydrogen atom are 3. The
emission transitions between these states will be
(1)3 (2)4 (3)5 (4)6
Ans. (4)
Sol. By using2
)1(
nnN E 6
2
)14(4
EN
Q.45 In Bohr’s model of hydrogen atom, let PE represents
potential energy and TE the total energy. In going to a
higher level
(1) PE decreases, TE increases
(2) PE increases, TE increases
(3) PE decreases, TE decreases
(4) PE increases, TE decreases
Ans. (2)
Sol. As n increases P.E. increases and K.E. decreases
Q.46 The third line of Balmer series of an ion equivalent to
hydrogen atom has wavelength of 108.5 nm. The
ground state energy of an electron of this ion will be
(1) 3.4 eV (2) 13.6 eV
(3) 54.4 eV (4) 122.4 eV
Ans. (3)
Sol. For third line of Balmer series 21 n , 52 n
22
21
2 111
nnRZ
givesRnn
nnZ
)( 21
22
22
212
On putting values Z = 2
From eVn
ZE 4.54
)1(
)2(6.136.132
2
2
2
Q.47 When hydrogen atom is in its first excited level, its
radius is .... its ground state radius
(1) Half (2) Same
(3) Twice (4) Four times
Ans. (2)
Sol. 2nr . For ground state n=1 and for first excited state
wavelength produced is
(1) 0.5 Å (2) 0.75 Å
(3) 0.25 Å (4) 1 Å
Ans. (3)
Sol. ÅÅ 25.0247.01050
123753min
.
Q.49 The voltage applied across an X-rays tube is nearly
(1) 10 V (2) 100 V
(3) 10000 V (4) 106 V
Ans. (3)
Sol. The voltage applied across the X-ray tube is of the
range of 10 kV – 80 kV.
Q.50 The shortest wavelength of X-rays emitted from an X-
ray tube depends on the
(1) Current in the tube
(2) Voltage applied to the tube
(3) Nature of gas in the tube
(4) Atomic number of target material
Ans. (2)
Sol. .mineV
hc where h, c and e are constants. Hence
V
1min
Q.51 The wavelength of X-rays is of the order of
(1) Centimetre
(2) Micron (10-6 m)
(3) Angstrom (10-10 m)
(4) Metre
Ans. (3)
Sol. Range of X-rays is 0.1Å to 100 Å.
Q.52 X – rays and rays of the same energies may be
distinguished by
(1) Their velocity
(2) Their ionising power
(3) Their intensity
(4) Method of production
Ans. (4)
Sol. The production of X-rays is an atomic property whereas
the production of -rays is a nuclear property
Q.53 The X-ray beam coming from an X-ray tube will be
(1) Monochromatic
(2) Having all wavelengths smaller than a certain
maximum wavelength
(3) Having all wavelengths larger than a certain
minimum wavelength
(4) Having all wavelengths lying between a minimum
and a maximum wavelength
Ans. (3)
n=2.
Classification of X’ray, continuous X’ray
Q.48 An X-ray tube is operated at 50 kV. The minimum
Modern Physics
E28-7
(1) The electrons are accelerated to a fixed energy
(2) The source of electrons emits a monoenergetic
beam
(3) The bombarding electrons knock out electrons from
the inner shell of the target atoms and one of the outer
electrons falls into this vacancy
(4) The valence electrons in the target atoms are
removed as a result of the collision
Ans. (3)
Q.55 Molybdenum is used as a target element for production
of X-rays because it is
(1) A heavy element and can easily absorb high
velocity electrons
(2) A heavy element with a high melting point
(3) An element having high thermal conductivity
(4) Heavy and can easily deflect electrons
Ans. (2)
Sol. In X-ray tube, target must be heavy element with high
melting point.
Q.56 Mosley’s law relates the frequencies of line X-rays
with the following characteristics of the target element
(1) Its density
(2) Its atomic weight
(3) Its atomic number
(4) Interplaner spacing of the atomic planes
Ans. (3)
Sol. 22 )()( bZabZ
Z = atomic number of element (a, b are constant).
Q.57 The wavelength of the K line of characteristic X-
ray spectra varies with atomic number approximately
(1) Z (2) Z
(3) 2
1
Z (4)
Z
1
Ans. (4)
Sol. Nucleus of heavy atom captures electron of k-orbit.
This is a radioactive process, so vacancy of this
electron is filled by an outer electron and x-rays are
produces.
Q.58 Mosley measured the frequency (f) of the characteristic
X-rays from many metals of different atomic number
(Z) and represented his results by a relation known as
Mosley’s law. This law is (a, b are constants)
(1) 2)( bZaf (2) 2)( bfaZ
(3) )(2 bZaf (4) 2/1)( bZaf
Ans. (1)
Sol. Mosley’s law is 2)( bZaf
Q.59 For harder X-rays
(1) The wavelength is higher
(2) The intensity is higher
(3) The frequency is higher
(4) The photon energy is lower
Ans. (3)
Q.60 The wavelength of K line for an element of atomic
number 43 is . Then the wavelength of K line for an
element of atomic number 29 is
(1) 29
43(2)
28
42
(3) 4
9(4)
9
4
Ans. (3)
Sol. 2)1(
1
Z
2
2
1
1
2
1
1
Z
Z
22
2
28
42
129
143
4
92 .
Characteristic X’ray
Q.54 The characteristic X-ray radiation is emitted, when
Modern Physics
E28-8
Q.1 Let nrand n
bbe respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time.
(1) nr= n
b(2) n
r< n
b(3) n
r> n
b(4) data insufficient
Ans. (3)
Sol.12400( eV)
E=
λ( inÅ)
IAt λNo. of Photon=
hc
Eλ
hc
PtλNo. ofPhoton= =
hc
if E is constant no. of photon is l
Q.2 The stopping potential for the photo electrons emitted from a metal surface of work function 1.7eV is 10.4 V. Identify the
energy levels corresponding to the transitions in hydrogen atom which will result in emission of wavelength equal to
that of incident radiation for the above photoelectric effect
(1) n = 3 to 1 (2) n = 3 to 2 (3) n = 2 to 1 (4) n = 4 to 1
Ans. (1)
Sol.hf =1.7+10.4=12.1eV=energy
in H-atom
12.09 ev
x = 3
n = 1
Q.3 A photon of light enters a block of glass after travelling through vacuum. The energy of the photon on entering the glass
block
(1) increases because its associated wavelength decreases
(2) Decreases because the speed of the radiation decreases
(3) Stays the same because the speed of the radiation and the associated wavelength do not change
(4*) Stays the same because the frequency of the radiation does not change
Ans. (4)
Sol. Frequency of light does not change with medium.
Q.4 If the frequency of light in a photoelectric experiment is doubled then maximum kinetic energy of photoelectron
(1) be doubled (2) be halved
(3*) become more than double (4) become less than double
Ans. (3)
Sol. Einstein's formula
kmax 1
= eV1+ f
if frequency is doubled,
kmax 2
= ev2
+ f > 2 Kmax 1
Q.5 Two separate monochromatic light beams A and B of the same intensity (energy per unit area per unit time) are falling
normally on a unit area of a metallic surface. Their wavelength are A
and B
respectively. Assuming that all the incident
light is used in ejecting the photoelectrons, the ratio of the number of photoelectrons from beam A to that from B is
(1*)
A
B
(2)
B
A
(3)
A
B
2
(4)
B
A
2
EXERCISE-II
Modern Physics
E28-9
Ans. (1)
Sol. The number of photo electron depends on the number of photons
Number of photon =/hc
I=
hc
·Iµ l
Ratio of no. of photo electrons =B
A
Q.6 When a photon of light collides with a metal surface, number of electrons, (if any) coming out is
(1) only one (2) only two (3) infinite (4) depends upon factors
Ans. (1)
Sol. A Photon can interact with only a single electron.
Q.7 The energy of a photon of frequency n is E = hn and the momentum of a photon of wavelength l is p = h/l. From this
statement one may conclude that the wave velocity of light is equal to :
(1) 3 × 108 ms–1 (2*)p
E(3) E p (4)
2
p
E
Ans. (2)
Sol. C = l · n =p
h·
h
E=
p
E
Q.8 Let p and E denote the linear momentum and the energy of a photon. For another photon of smaller wavelength (in same
medium)
(1*) both p and E increase (2) p increases and E decreases
(3) p decreases and E increases (4) both p and E decreases
Ans. (1)
Sol. Applying p =
hand E =
hc
If l decreases E and p increases.
Q.9 Radiation of two photon energies twice and five times the work function of metal are incident sucessively on the metal
surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be
(1) 1 : 2 (2) 2 : 1 (3) 1 : 4 (4) 4 : 1
Ans. (1)
Sol.
1 22 1 1 12
1 25 42 2 22
: 1 : 21 2
K K mv
K K mv
v v
Q.10 By increasing the intensity of incident light keeping frequency (v > v0) fixed on the surface of metal
(1) kinetic energy of the photoelectrons increases
(2) number of emitted electrons increases
(3) kinetic energy and number of electrons increases
(4) no effect
Ans. (2)
Sol. no. of Photons I
I , no. of photon e- ejection
Modern Physics
E28-10
Q.11 If h is Planck’s constant is SI system, the momentum of a photon of wavelength 0.01 Å is:
(1) 10–2 h (2) h (3) 102 h (4) 1012h
Ans. (4)
Sol.12h
=10 hλ
statements.
(i) The saturation photocurrent remains almost the same.
(ii) The maximum kinetic energy of the photoelectrons is doubled.
(1) Both (i) and (ii) are true(2*) (i) is true but (ii) is false
(3) (i) is false but (ii) is true (4) both (i) and (ii) are false
Ans. (2)
Sol. Since frequency of light solurce is double, the energy carried by each photon will be doubled.
Hence intensity will be doubled even if number of photons remains constant. Hence saturation current is constant. Since
frequency is doubled, maximum KE increases but it is not doubled.
Q.13 The work function for aluminium surface is 4.2 eV and that for sodium surface is 2.0 ev. The two metals were illuminated
with appropriate radiations so as to cause photo emission. Then :
(1) Both aluminium and sodium will have the same threshold frequency
(2*) The threshold frequency of aluminium will be more than that of sodium
(3) The threshold frequency of aluminium will be less than that of sodium
(4) The threshold wavelength of aluminium will be more than that of sodium
Ans. (2)
Sol. The threshold frequency for Al must be greater as it has higher work function.
Q.14 The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV.
The stopping potential is :
(1) 2V (2*) 4V (3) 6V (4) 10V
Ans. (2)
Sol. Stopping potential = maximum kinetic energy of e = 4V.
Q.15 If the frequency of light in a photoelectric experiment is doubled, the stopping potential will
(1) be doubled (2) halved
(3) become more than doubled (4) become less than double
Ans. (3)
Sol. hf = +evs
Q.16 10–3 W of 5000 Å light is directed on a photoelectric cell. If the saturationcurrent in the cell is 0.16 mA, the
percentage of incident photons which produce photoelectrons, is
(1) 0.4% (2) 0.04% (3) 20% (4) 10%
Ans. (2)
Experimental study of photoelectric effect
Q.12 In a photoelectric experiment, the frequency and intensity of a light source are both doubled. Then consider the following
Modern Physics
E28-11
Sol.-3
10No.ofPhotons=
12400 -13×1.6×10
5000
16=0.25×10
-60.16×10- +12
No.of e reaching= =10-19
1.6×10
1210
%= ×100=0.04%16
0.25×10
Q.17 Which one of the following graphs in figure shows the variation of photoelectric current (I) with voltage (V) between
the electrodes in a photoelectric cell ?
(1*) (B) (C) (D)
Ans. (1)
Sol. Experimental obervation.
Q.18 When a centimetre thick surface is illuminated with light of wavelength , the stopping potential is V. When the same
surface is illuminated by light of wavelength 2, the stopping potential is V/3. The threshold wavelength for the surface
is :
(1)3
4(2*) 4 (3) 6 (4)
3
8
Ans. (2)
Sol.
hC= + eV ....(i)
2
hC= +
3
eV....(ii)
3 · II – I
1–
2
3
hc= 2 =
4
hc
th
=4
Modern Physics
E28-12
Q.19 A point source causes photoelectric effect from a small metal plate. Which of the following curves may represent the
saturation photocurrent as a function of the distance between the source and the metal?
(1)
i
t
(2)
i
t
(3)
t
i
(4)
i
t
Ans. (4)
Sol. As distance ses.
I ses.
i
24
PI
r
Q.20 In a photoelectric experiment, electrons are ejected from metals X and Y by light of intensity I and frequency f. The
potential difference V required to stop the electrons is measured for various frequencies. If Y has a greater work function
than X ; which one of the following graphs best illustrates the expected results ?
(1)
o f
v
X
Y (2)
o f
v
X
Y(C)
o f
v
X
Y (4)
o f
v
XY
Ans. (1)
Sol. Greater work function means greater cut off frequency.
Slope Remains same
fy>f
x
Intercept of y > Intercept of x
and must be parallel to each
Q.21 A image of the sun of formed by a lens of focal-length of 30 cm on the metal surface of a photo-electric cell and a
photo-electric current is produced. The lens forming the image is then replaced by another of the same diameter but
of focal length 15 cm. The photo-electric current in this case is
(1) I/2 (2) I (3) 2I (D) 4I
Ans. (2)
Sol. Diameter is same so light falling will be same so photoelectric current will be same.
Q.22 When ultraviolet light is incident on a photocell, its stopping potential is V0
and the maximum kinetic energy of the
photoelectrons is Kmax. When X-rays are incident on the same cell, then :
(1*) V0
and Kmax
both increase (2) V0
and Kmax
both decrease
(3) V0
increases but Kmax
remains the same (4) Kmax
increases but V0
remains the same
Ans. (1)
Sol. The energy of x–ray is more that of U.V. light. Hence, the K.E. of emitted photoelectron is more and hence stopping
potential required is also more.
Modern Physics
E28-13
8 ms–1 is equal to that of a photon. The ratio
of the kinetic energy of the electron to that of the energy of photon is :
(1)2(2)4 (3)2
1(4*)
4
1
Ans. (4)
Sol. ld =mv
h
El = energy of photon =
hcand energy of e– =
m2
p2
=2
hv
The required ratio =4
1
hc2
hv
.
Q.24 The de Broglie wavelength of a neutron correspoding to root mean square speed at 927ºC is . What will be the de
Broglie wavelength of the neutron correspoding to root mean square speed at 27ºC?
(1)2
(2) (3*) 2 (4) 4
Ans. (3)
Sol. K.E. of neutron E =2
3kT
d =p
h=
mE2
h= kT
2
3m2
h
; 2 =27327
)273927(.
= 2.
Q.25 The wavelength of de Broglie waves associated with an electron (mass m, charge e) accelerated through a potential
difference of V is given by (h is Planck’s constant) :
(1) = h/mV (2) = h/2 meV (3) = h/ meV (4*) = h/ meV2
Ans. (4)
Sol. =P
h=
mK2
h=
meV2
h
Q.26 A proton and an electron are accelerated by same potential difference have de-Broglie wavelength p
and e.
(1)e=
p(2)
e<
p(3)
e>
p(4) none of these
Ans. (3)
Sol. They have same K.E.
hλ=
2m K.E.
mp> m
eand q
p=q
e
p<
eas
1
m
Q.27 An electron with initial kinetic energy of 100eV is acceleration through a potential difference of 50V. Now the de-
Broglie wavelength of electron becomes.
(1) 1 Å (2) 1 5. Å (3) 3 Å (4) 12.27 Å
Ans. (1)
De-Broglie Wavelength.
Q.23 The de Broglie wavelength of an electron moving with a velocity 1.5 × 10
Modern Physics
E28-14
Sol. KE =100+50 =150eV
v =150volt
150λ =
V
0
A1
(1) 4a0
(2) a0
(3) a0/4 (4) a
0/16
Ans. (2)
Sol. r = a0 Z
n2
= a0.
4
22
= a0
Q.29 Which energy state of doubly ionized lithium (Li++) has the same energy as that of the ground state of hydrogen ?
Given Z for lithium = 3 :
(1) n = 1 (2) n = 2 (3*) n = 3 (4) n = 4
Ans. (3)
Sol. En(Li2+) = E
1(H)
– 13.6 2
2
n
3= –13.6 ×
1
1
n = 3
Q.30 The angular momentum of an electron in the hydrogen atom is3
2
h
. Here h is Planck’s constant. The kinetic energy of
this electron is :
(1) 4.53 eV (2) 1.51 eV (3) 3.4 eV (4) 6.8 eV
Ans. (2)
Sol. L
nhJ = mvr =
2
n = 3
1K.E. = - T.E. = 13.6 ×
9
=1.51ev
Q.31 The innermost orbit of the hydrogen atom has a diameter of 1.06 Å. What is the diameter of the tenth orbit ?
(1) 5.3 Å (2) 10.6 Å (3) 53 Å (4*) 106 Å
Ans. (4)
Sol. r n2
r10 = 102 × 1.06 Å = 106 Å.
Bohr’s model
Q.28 If a0
is the Bohr radius, the radius of the n = 2 electronic orbit in triply ionized beryllium is -
Modern Physics
E28-15
Q.32 Consider the following electronic energy level diagram of H-atom : Photons associated with shortest and longest
wavelengths would be emitted from the atom by the transitions labelled.
B
CD
n=
n=4
n=3
n=2
n=1
A
(1) D and C respectively (2) C and A respectively
(3) C and D respectively (4) A and C respectively
Ans. (3)
Sol.2
2 21 2
1 1 hcE Rcz
n n
C Shortest
D longest
Q.33 If an orbital electron of the hydrogen atom jumps from the ground state to a higher energy state, its orbital speed
reduces to half its initial value. If the radius of the electron orbit in the ground state is r, then the radius of the new
orbit would be :
(1) 2r (2*) 4r (3) 8r (4) 16r
Ans. (2)
Sol. Since speed reduces to half, KE reduced to
4
1th n = 2
mvr =2
nh
mv0r = 1.
2
h..........I
m2
v0r` = 2 ·
2
h.........II
from I and II
r´ = 4r
Q.34 In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in a quantum
state n is :
(1*) – 1 (2) + 1 (3)n1
(4) 2
1
n
Ans. (1)
Sol. According to the Bohr model
P.E. = – 2 K.E. = 2 T. E.
K.E. = – T.E.
Modern Physics
E28-16
Where T.E. =222
0
4
hn8
me–
K. E.= – 2220
4
hn8
me–
.E.T
.E.K= –1
Q.35 Three photons coming from emission spectra of hydrogen sample are picked up. Their energies are 12.1eV, 10.2eV
and 1.9eV. These photons must come from
(1) a single atom (2) two atoms
(3) three atom (4*) either two atoms or three atoms
Ans. (4)
Sol. 12.1 = E(n = 3) – E (n = 1)
10.2 = E(n = 2) – E (n = 1)
1.9 = E(n = 3) – E (n = 2)
At least two atoms must be enveloped as there connot be two transition from same level from same atom.
Q.36 In a hypothetical atom, if transition from n = 4 to n = 3 produces visible light then the possible transition to obtain
infrared radiation is :
(1) n = 5 to n = 3 (2) n = 4 to n = 2 (3) n = 3 to n = 1 (4*) none of these
Q.37 The ionization energy of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by electromagnetic
radiation of energy 12.1 eV. How many spectral lines will be emitted by the hydrogen atoms?
(1) one (2) two (3*) three (4) four
Ans. (3)
Sol 12.1 eV radiation will excite a hydrogen atom in ground state to n = 3
state number of possible transition = nC2
= 3C2
= 3.
Q.38 If the electron in a hydrogen atom were in the energy level with n = 3, how much energy in joule would be required to
ionise the atom ? (Ionisation energy of H-atom is 2.18 × 10–18 J):
(1) 6.54 × 10–19 (2) 1.43 × 10–19 (3) 2.42 × 10–19 (4) 3.14 × 10–20
Ans. (3)
Sol.
18
2
2.18 10I.E.
n
182.18 10
9
= 2.42 × 10-19 J
Q.39 Difference between nth and (n + 1)th Bohr’s radius of ‘H’ atom is equal to it’s (n – 1)th Bohr’s radius. The value of n
is :
(1)1(2)2 (3)3 (4)4
Ans. (4)
Sol. 2 22
2
0.529 1 0.529 1
2 1 1 2
0, 4
n n n
n n n
n
Ans. (4)
Sol. All the transition energies in option(1),(2) and (3) are greater than corresponding to n = 4 to n = 3. Hence, option (4).
Modern Physics
E28-17
Q.40 The wavelength of the first line in balmer series in the hydrogen spectrum is . What is the wavelength of the second
line :
(1*)27
20(2)
16
3(3)
36
5(4)
4
3
Ans. (1)
Sol.1
1
= R
9
1–
4
1 l
1=
R5
94
similarly2
1
= R
24
1–
4
1 l
2=
R3
16=
3
16×
94
5
=
27
20
Q.41 The frequency of the first line in Lyman series in the hydrogen spectrum is n. What is the frequency of the corresponding
line in the spectrum of doubly ionized Lithium ?
(1) n (2) 3 n (3*) 9 n (4) 27 n
Ans. (3)
Sol. E = 13.6
2
2
n
Z
D EH = 2
2
)1(
)1(6.13– 2
2
)2(
)1(6.13= 10.2 eV = hn
DELi = 2
2
)1(
)3(6.13– 2
2
)2(
)3(6.13= 91.80 eV = h (9 n)
Q.42 In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various
energies is passed. In absorption spectrum, five dark lines are observed. The number of bright lines in the emission
spectrum will be (Assume that all transitions take place)
(1)5(2)10 (3)15 (4) none of these
Ans. (3)
Sol. n - 1 = 5
n = 6
No. of briught lines = n n 1
2
=
6 5
2
= 15
Q.43 When a hydrogen atom, initially at rest emits, a photon resulting in transition n = 5 n = 1, its recoil speed is about
(1) 10–4 m/s (2) 2 × 10–2 m/s (3) 4.2 m/s (4) 3.8 × 10–2 m/s
Ans. (3)
Sol.E
PC
n1
= 1, n2= 5
2 219
8
13.6 13.6
1 51.6 10
3 10
2713.0561.6 10
3
mv = 6.96 × 10-27
v = 4.2 m/s
Modern Physics
E28-18
Q.44 Consider the spectral line resulting from the transition n = 2 n = 1 in the atoms and ions given below. The shortest
wavelength is produced by :
(1) hydrogen atom (2) deuterium atom
(3) singly ionized helium (4) doubly ionized lithium
Ans. (4)
2
2
2 21 2
2
1 1 hcΔE=Rcz - =
n n λ
1z
λ
For z = 3 Li
λwill be minimum
Q.45 The electron in a hydrogen atom make a transition from an excited state to the ground state. Which of the following
statement is true?
(1) Its kinetic energy increases and its potential and total energies decrease
(2) Its kinetic energy decreases, potential energy increases and its total energy remains the same.
(3) Its kinetic and total energies decrease and its potential energy increases.
(4) Its kinetic potential and total energies decreases.
Ans. (1)
Sol. T.E.=P.E. + K.E.
Existed
Ground
E
So both P.E. & K.E.
Q.46 Radius of the second Bohr orbit of singly ionised helium atom is
(1) 0.53 Å (2) 1.06 Å (3) 0.265 Å (4) 0.132 Å
Ans. (2)
Sol.2
2
2
0
nr = 0.529 ×
Z
20.529×
r =1.06 A
Q.47 An electron in Bohr’s hydrogen atom has an energy of –3.4 eV. The angular momentum of the electron is
(1) h/ (2) h/2
(3) nh/2 (n is an integer) (4) 2h/
Ans. (1)
Sol. E = -3.4 ev (for n = 2)
n = 2
angular momentum =
2h h
2
Modern Physics
E28-19
(1*) the kinetic energy of the stricking electron
(2) the kinetic energy of the free electrons of the target
(3) the kinetic energy of the ions of the target
(4) an atomic transition in the target
Ans. (1)
Sol. The contineous x-ray comes out because the striking electron lose its kinetic energy
Q.50 If the voltage across the filament is increased, the cutoff wavelength
(1) will increase (2) will decrease (3*) will remain unchanged (D) will change
Ans. (3)
Sol. The cut off wavelength depends on the accelerating potential difference which is unchanged. Hence, the wavelength
will remain unchanged.
Q.51 Which of the following wavelength falls in a X-rays region?
(1) 10,000 Å (2) 1000 Å (3) 1 Å (4) 10–2 Å
Ans. (3)
Sol.0
0.1 to 10 A (x-ray range)
Q.52 The penetrating power of X-ray increases with the
(1) Increases of its velocity (2) Increase in its intensity
(3) Decrease in its velocity (4) Increases in its frequency.
Ans. (4)
Sol. When freqency is increased energy increases
i.e. penetrating power increases
1and m
2, having non zero velocities. The ratio of the
de Broglie wavelengths of the particles, 1/
2is :
(1)2
1
m
m(2)
1
2
m
m(3*) 1 : 1 (4)
1
2
m
m
Ans. (3)
Sol =p
h
Since the momenta of the two particles are equal, are same.
Q.54 Consider a metal used to produced some charateristic X-rays. Energy of X-rays are given by E and wavelength as
represented by . Then which of the following is true :
(1)E(K) > E(K
) > E(K
) (2) E(M
) > E(L
) > E(K
)
(3*)(K) >(K
) >(K
) (4*)(M
) >(L
) >(K
)
Ans. (3)
Ans. (1)
Sol. In ultra violet region lyman series is present
Classification of X’ray, continuous X’ray
Q.49 Consider a photon of continuous X-ray coming from a Coolidge tube. Energy of photon comes from
Characteristic X’ray
Q.53 A particle of mass M at rest decays into two particles of masses m
Q.48 If radiation of allow wavelengths from ultraviolet to infrared is passed through hydrogen agas at room temperature,
absorption lines will be observed in the :
(1) Lyman series (2) Balmer series (3) Both (1) and (2) (4) neither (1) nor (2)
Modern Physics
E28-20
Sol. K
: transition from 2 1
Similarly for K
: 3 1 , K: 4 1 ; L
0: 3 2 : M
: 4 3
Now we can compare energy and .
Q.55 The characteristic X-ray spectrum is emitted due to transition of
(1) valence electrons of the atom
(2*) inner electrons of the atom
(3) nucleus of the atom
(4) both, the inner electrons and the nucleus of the atom
Ans. (2)
Sol. The characteristic x-rays are obtained due to the transition of electron from inner orbits.
Q.56 In a characteristic X-ray spectra of some atom superimposed on continuous X-ray spectra
PQ
Rel
ativ
ein
tens
ity
(1) P represents K
line
(2) Q represents K
line
(3) Q and P represents K
and K
lines respectively
(4) Relative positions of K
and K
depend on the particular atom
Ans. (3)
Sol.
p q
P Q
K K
hc hcE
E
E E
E E
So Q K
P K
Q.57 In X-ray tube, when the accelerating voltage V is doubled, the different between the wavelength of K line and the
minimum cut off of continuous X-ray spectum :
(1) remains constant (2) becomes more than two times
(3) becomes half (4) becomes less than 2 times.
Ans. (2)
Sol. When ever the energy of photon is doubled then work function increases must more than by 2 times.