module 1 - em radiation and quantum ms (2) (1)

7/26/2019 Module 1 - Em Radiation and Quantum Ms (2) (1)

1/23

1. (a) (i) electronvolt is the energy gained (1)

by an electron moved through a p.d of 1 V (1)

(ii) 2

1

m2= eV(1)

2=

31

19

11.9

!1!.12

(1)= ".! #17ms

14

(b) electrons can behave like waves and like particles (1) 1[5]

2. (a) (i) hf = photon energy (1)

(ii) f= minimumenergy to eject electron from metal surface (1)

(iii) Ek= maximumkinetic energy of a photoelectron (1) 3

(b) (i) no photoelectrons are emitted (1)

(ii) wave theory predicts photoelectrons will be emitted withred light (or at any freuency) (1)

(iii) one photon absorbed by one electron (1)electron emitted from metal if photon energy!or hf" # f(or not if $ f) (1)

red light photon energy $ f(1) ma% 3

(c) f=

hc

(1)k&e&ma%(1)

f=$

%3"

1.3

1.31!3.!

3.2! # 119

(1)

f= 3&4 #119

' (1) [8]

3. (a) u

=

m

E2

=31

1%

11.9

1.22

(1)

= &1# 1m s

1(1)

(b) (i) difference between E and E* = 1&+4 # 11%

' (1)

which is less than the electron kinetic energy (1)

King Edward VI Five Ways School 1


2/23

(ii) (, &1) = 3&* # 119

(1)(=

hc

)

l=19

%3"

1!.3

1.31!3.!

(1)= &- # 1$

m (1)in visible !or red" region (1)

(c) for ionisation. p&d& =19

19

1!.1

1%.21

(1)=13& / (1) [10]

4. (a) u= m

h

(1)

=131

3"

1'.111.9

1!3.!

= 4&0 # 1ms

1(1)

(b) yes (1)same order as l(1)

[4]

5. (a) mean k&e& (= 2

3

kT= 1&- # 1.3% # 123

# 2) = "(.1) # 123

' (1)

(b) m

=

2312.!

".

= & # 12$

(kg)

2

1

mu(or 2

1

# !.! # 12$

# u)= 4&1 #1

23' (1)

u

=2$

23

1!.!

11."2

= 11*(ms1

)

!or mu=( )

2

1232$ 11."1!.!2

= 7&4 # 12'

kg m s1

" (1)

l= m

h

(or 111!.!

1!.!2$

3"

or2'

3"

1".$

1!.!

) (1)

= 0&+ # 11

m (1)see below for alternative to b!

(c) de roglie wavelength is of the order of the si2e of the atom(at very low temperatures) (1)

King Edward VI Five Ways School "


3/23

alternative b!

l= meV

h

2 or 2mE

h

(1)

eVor E= 4&1 # 123

(') (1)

m= & # 12$

(kg) (1)

l=232$

3"

11."1!.!2

1!.!

(1)

l= 0&+ # 11

m (1)[Max 6]

6. (a) only certain energies !or energy changes" allowed (1)a line !or photon" corresponds to transition between levels (1)each transition !or energy change"corresponds to a definite wavelength !or freuency" (1) 3

(b) (i) Eion= 1*&4# 1.! # 119

(or1*&4 e/) (1)

= 1& # 11%

(') (1)

(ii) E

=

hc

=9

%3"

11"1

1.31!.!

(1)

= 1&4* # 11%' (1)= 0&0 e/ (1)which is from 1& to 1*&4 (1)

(iii) ultra5violet (1) 7[10]

King Edward VI Five Ways School #


4/23

7. (a) (i) electrons behave sometimes as particles. sometimes as waves (1)

(ii) $article e%am$le& deflection in electric !or magnetic" field (1)

wave e%am$le& diffraction (1) 3

(b) (kinetic energy) 2

1

m'eV(1)

p(= m) = m

eVm

2

(1) meV2=

l = p

h

. gives result (1) 3[6]

8. (a) fis minimum energy needed to remove electron (1)Ek is ma%imum energy of emitted electron (1)

(b) (i) Ek= hff

f=

c

6 Ek= hc

1

f(1)

cf y= m% c(1)

(ii)

l8 nm ** 3** 4** -** **

Ek# 119

' &7 3&3* 1&0 *& *&*-

1

8 nm1

*&**-* *&**33 *&**- *&*** *&**17

1

values correct (1)

both a%es correctly labelled (1)five points correctly plotted (1)sensible scale and straight line (1)

King Edward VI Five Ways School (


5/23

graph for uestion -

7

6

5

4

3

2

1

0

1

2

3

4

0 . 0 0 1 0 . 0 0 2 0 . 0 0 3 0 . 0 0 4 0 . 0 0 5

E # 1 )* 1 9

1

+ n m 1

from intercept. f= 3&3 # 119

' (1)= &1 e / (1)

use of large triangle gives gradient

=!

19

1)!'.1.'(

1$.!

= &*1 # 12'

h= c

gradient

= &7 # 13"

' s (1) ma% +

King Edward VI Five Ways School )


6/23

(c) straight line to right of present curve (1)parallel to it (1)

(d) ultraviolet high freuency (1)

above f* for emission (1)!or red light low freuency (1)below f*for emission (1)"

!alternatived!ultraviolet !red light" photon energy is high !low" (1)above !below" work function (1)"

[15]

9. (a) (i)

c o n d e n s e r l e n s

o b , e c t i v e l e n s

t h i r d m a g n e t i c l e n s

crossed rays after third lens (1)image arrow same way round as sample (1)

(b) (i) to make a (wide) parallel beam of electrons!or to direct electrons straight at the sample" (1)to ensure the beam is uniform across its width!or across the sample" (1)

(ii) to form a magnified image (of the sample) (1)

(iii) to magnify the image further (1)to form the image on a screen (1) ma% 3

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7/23

(c) (i) resolving power increases with !proportional to"increase of the accelerating p&d& (1)electron wavelength becomes smaller the greater the p&d& (1)resolving power is greater the smaller the wavelength (1)

(ii) lens aberrations !or defects" (1)caused by electrons having a range of speeds!repelling each other" (1)!or sample thickness (1)which causes loss of electron speed (1)" ma% 4

[9]

10. (a) F work function (1)minimum energy (1)

reuired to remove an electron (from the photocathode)(1)(or energy reuired to remove electron from surface)

ma%imum kinetic energy (1)

Ek of emitted (photo)electron (leaving the metal)(1) -

(b) (i) 4&(*) m9 (1)doubling the intensity doubles the number of photons (per se) (1)(which) doubles the number of electrons released (per se) (1)current = rate of flow of charge (1)assume one photon liberates one electron (1)(or assume all the photoelectrons are collected) (1)

(ii) (fo= cllogives)fo= 3&* # 1%

83-* # 19

(1)

= 0& # 114

:2 (1) (0&-7 # 114

:2)(1)

(F= hfogives) F= &(3) # 13"

# %.'$ # 114

(allow e&c&f& for fo)

= -&7 # 119

' (1) (-&0 # 119

')(1) ma% -[10]

11. (a) need for e%citation (1)electrons in an atom can only e%ist at definite8discrete energylevels8orbits (1)an electron falls from one level to another (1)photon emitted (1)photon has definite wavelength (1) ;


8/23

(b) (i) an electron is removed from a (neutral) atom (1)

(ii) & # 11%

(') (1)

(iii) (fmin'E8hgives)fmin= & # 11%

8&(3) # 13"

(1)

(allow e&c&f from result of (b)(ii))(1)

= 3&3() # 11-:2 (1)

(iv) ionised electron gains kinetic energy(or electron breaks free of atom) (1) -

(c)3"

191912

1)3(!.!

1".21".'gives

)(

=

= fh

EEf

(1) (= 4&- # 114

:2)

(l= c,fgives) l'3&* # 1084&- # 1

14(1)(allow e&c&f& for f)

= &(3) # 1$

m (1) 3[11]

12. (a) (i) (wave property) (electron) diffraction (1)

(ii) (particle5property) photoelectric effect (1)

(iii) (wave property) interference8diffraction8refraction (1) 3

(b) (momentum of electron = ) mu = +&11 # 131

# '. # 1(1)

(= 4&- # 12"

(kg ms1

))(1)

!(l ' h,m ugives) l= &(3) # 13"

84&- # 12"(1)

(allow e&c&f for value of mu!

=1&- # 11

m (1) (1&4- # 11

m) 3[6]

13. (a) electrons move(or e%cited) from one energy level(or orbit) to another (1)

emitting or absorbing a definite freuency8wavelength8colour (1)or photon energy(of electromagnetic radiation) (1)

;


9/23

(b) (i) Ei= -&(e/) (1) # 1.! # 119

= 0&3 # 119

(') (1)(allow e&c&f& if incorrect value of energy in e/)

(ii) (f=

c

gives) f=$

%

11.!

1.3

(1)

= 4&+ # 114

:2 (1)

(iii) (>E= hfgives) E= &3 # 13"

# ".9 # 114

(1)

= 3& # 119

(') (1)(allow e&c&f from(ii))

(iv) line drawn from Bto D(1)

(v) > to , (1)

(vi) to (1) +[11]

14. (a) (i) electromagnetic radiation behaves either as a particle or as a wave (1)

(ii) (electromagnetic radiation) behaves as a particle (1)

(b) (i) hf=. Ek(1)

.= (&3 # 13"

# 1.!$ # 11-

) (3. # 119

) (1)

= 0&1 # 119(1) ' (1) (0&*7 # 119)

(ii) (number per second) doubled (1)(ma%imum kinetic energy) remains constant (1)

(iii) (all) electrons have insufficient energy to leave the (new) metal (1)the work function of the (new) metal is greater than hf!or the work function of the (new) metal is greater thanthat of the original metal" (1) 0

;


10/23

(ii) (use of E= hfgives) E= &3 # 13"

# 9.$ #114

(1)

= &43 # 119

(') (1)

(iii) (use of hf= f Ekgives) &43 # 119

= f &4+ # 119

(1)

(allow &,& from (b)(ii))

f = 3&+4 # 119

(') (1)

(iv) f =

19

19

1!.1

19".3

= &4 (e/) (1)(allow &,& from (b)(iii) 7[10]

16. (i) an electron is removed from the atom (1)

(ii) &10 # 11%

(') (1)

(iii) (single photon)electron loses energy !or falls" from level n= 3 to n= 1and emits a single photon (1)

(two photons) electron falls from level n= 3 to n= .emitting a photon (1)followed by a fall from level n= to n= 1. emitting another photon (1) ;


11/23

(c) (i) (use of hf= E1 Egives) f=

( )3"

1%1%

1!3.!

1'9.12!.

(1)

= -&* 1*14:2 (1)

(ii) line joining level n= 3 to level n= with arrow pointing down (1) 3[8]

18. (a) (i) the energy of a photon does not depend on the intensity (1)so electron gains no e%tra energy!or the energy is dependent on the wavelength8freuency" (1)

(ii) the intensity of the light determines the number of photonsper second (1)

one photon interacts with one electron!or hence more interactions with electrons" (1) 3

(b) (i) (use of c= flgives) f=$

%

11.'

1.3

(1)

= -&00 1*14(:2) (1)

(ii) (use of E= hfgives) E= &3 1*3"-&00 1*14 (1)(allow &,& for value of ffrom (i))

= 3&+(*) 1*19(') (1)

(iii) (use of hf= f Ekgives) 3&+ 1*19

= 3&-0 1*19 Ek (1)(allow &,& for value of Efrom (ii))

Ek= 3& 1*2

(') (1)

(iv) caesium (1) (allow &,& for value of Efrom (ii)) 7[10]

19. (i) speed of electron = 1

1.3.2 %

(1)(=&** 1*(m s1))

(use of

= h

m gives)!31

3"

1.!111.9

1!3.!

=

(1)

= 1&1 1*1m (1)

King Edward VI Five Ways School 11


12/23

(ii) (use of c= flgives) f=1

%

121.1

1.3

(1)(allow &,& for value of lfrom (i))

= &40 1*10:2 (1) -[5]

20. (a) electron diffraction or interference (1) 1

(b) (use of l= mv

h

gives) l ='31

3"

1.'111.9

1!3.!

(1)

= 1&4 # 19

m (1)

(c) mm= *7 # 9.11 # 131(kg) (1) ( =

1&0+ 1*2%(kg))

(use of = meve= mmvm. = when l is constant. gives)

vm=2%

'13

1%9.1

1.'111.9

(1)

= &4 # 13m s

1(&41 # 1

3m s

1) 3

!or recalculate using v'

-1"!.11%9.1

1!3.!92%

3"

=m

h

(d) gain in energy or work done on particle is the same for both (1)wavelength is inversely proportional to momentum (1)gain in momentum is different for both (1)the smallest mass has the largest acceleration8gain in speed (1)

!or wavelength proportional to m

with constant k&e&" ma% [8]

21. (a) (i) electrons fall down from orbits or energy levels and emitlight8photons (1)emitted wavelengths8freuencies8photon energies arediscrete (1)!or the transitions are between definite8fi%ed (energy) levels (1)

(ii) (1)

(iii) between > and 9 (1)the two arrows must point down (1) ma% 4

King Edward VI Five Ways School 1"


13/23

(b) (i) (use of hf= E Elgives)

f=

3"

19

1!.!

13.2

= 3&- # 114

:2 (1)

f= 3& # 114

(:2) (1)

f= *&3 # 114

(:2) (1)

(ii) 4& # 119

(') (1)

=19

19

1!.1

1!."

= &+ (e/) (1) -[9]

22. (a) (i) the minimum energy (1)

energy reuired to eject a (photo)electron (from the metal surface) (1)

(ii) changing the metal8cathode (1) 3

(b) conclusion light below athreshold freuency does notrelease electrons (1)

e%planation photons carry uanta of energy (1)

!or conclusion electrons are emitted immediately thelight hits the metal surface (1)

e%planation photons carry uanta of energy (1)"

(c) (i) (use of E ' hf'

hc

gives) E=$

%3"

1%."

131!3.!

(1)

4&14 # 119

(')

(ii) hf= f Ek(1)

Ek= 4&14 # 119

1.2 # 119

(1)

= &+4 # 1

19

(') (1)(allow &, for value of Efrom (i)) -[10]

23. (a) there must be a large distance between collisions to allowelectrons to gain enough energy (1)!or the vapour must not completely absorb the electrons" 1

King Edward VI Five Ways School 1#


14/23

(b) the mercury vapour emits ultra violet (radiation) (1)the coating absorbs electromagnetic radiation8light from the mercury (1)emits longer wavelengths8lower freuencies in the visible region (1) ma% 3

;


15/23

(b) (use of l = mh

gives)

=

mhv

=131

3"

1$.1111.9

1!3.!

(1)

= 4&0 # 1m s

1(1)

[5]

27. (a) (use of hf= f Ekgives) 3& # 119

= f &1 # 119

f= 1&1 # 119

(1) ' (1) 3

(b) incident energy of each photon is doubled

&4 # 119

= 1&1 # 119

Ek

Ek= -&3 # 119

' (1) 3

[6]

28. (a) (i) an electron8atom in an energy level8state or an orbiting electron (1)is given energy (1)to move to a higher level or orbit (1)

(ii) electromagnetic radiation is emitted when an electron falls (1)from one fi%ed level to another fi%ed level (1)giving the photon a discrete amount of energy (1) ma% -

;


16/23

29. electrons diffract !or high energy electron scattering" (1)showing wave behaviour (1)

electrons are deflected in electric or magnetic fields (1)showing particle behaviour (1)

interference of electromagnetic waves (1)showing wave behaviour (1)

photoelectric effect (1)showing particle behaviour (1) ma%

;


17/23

32. (a) (i) k&e& =19

1%

1!.1

11."

(1)= (e/) (1)(-& e/)

(ii) (use of ld= mv

h

gives) ld=!31

3"

1.311.9

1!.!

(1)

= &4 # 11m (1) (&4 # 11m) 4

(b) (use of hf = E1 Egives) f=3"

1%

1!.!

1)21.9.(

(1)

(= 1&*- # 11-

(:2))

(use of l=f

c

gives) l=1'

%

1'.1

1.3

(1)

= &+ # 1$

m (1) (&0 # 1$

m) 3[7]

33. (a) (i) (named force) from weak (nuclear). electromagnetic or gravity (1)

uses a mediating8e%change particle. named particle from and > to (1)

both in correct order (1) [8]

40. (a) intensity determines the number of photons per second(1)fewer photoelectrons per second(1)(individual) photon energies are not changed(1)with no change in the (kinetic) energy8speed(1)

one photon interacts with one electron (1) 3

(b) energy of a photon is proportional to freuency (or E ' h.!(1)photon of red light has less energy than a photon of blue light!or8fred$8fblue or lred lblue2(1)

the energy is insufficient to overcome the work function of the metal!or the freuency is below the threshold freuency"(1) 3

(c) (i)

1'

9

%

1'.112

1.3=

=f:2(1)

(ii)3"

19

1!3.!

13.2

=

=

hf

(1)

=3&- # 114

:2 (1)

(3&47 # 114

:2)

(iii) (use of kEhf += gives)( ) 191'3" 13.21'.11!3.! kE (1)

7& # 119

(')(1)

(7&4- # 119

(')) -

allow 34E for value of f from i!![11]

41. (a) (i) (3&4*51&-1 = 1&0+)

5E' 1&0+ # 1.! # 119

(')(1)

(= 3&* # 119

('))

3"

19

1!3.!

12.3

=

= h

Ef

(1)

(=4&- # 114

:2)

King Edward VI Five Ways School "1


22/23

(ii)

m1)%('.!1'!."

1.3 $1"

%

=

==f

c

(1)

(use of f = 4& # 114

gives l' &- # 1$

m) 3

(b) (i) (wavelengths)(1)

(ii) (1&-1.%') = .!!(eV)(1)

(c) mercury vapour at low pressure is conducting(1)atoms of mercury are e%cited by electron impact(1)producing (mainly) ultra violet radiation(1)which is absorbed8 e%cites the coating(1)which. upon rela%ing. produces visible light(1)electrons cascade down energy levels(1) 3

[8]

42. (a) hf 'ph!nenergy (1)f= work function (1)Ek= maximumkinetic energy of photoelectrons (1) 3

(b) (i) E

=

hc

=$

%3"

1%.3

131!.!

= -&3 # 119

' (1)

(ii) energy on surface = &* # 112

' mm2

s1

(1)

6=1!

12

123.'

1.!

= 1&1(-) # 14s

1(1)

(iii) Ek

=

6

hc

=(-&(3)3.2) (1)# 119

= &* # 119

' (1) -

[8]

43. (a) inelastic collisions between electrons and atoms (1)energy of atom increases (1)atom emits photon. returns to original state (1) 3

(b) photon energy related to wavelength (1)discrete wavelengths suggest fi%ed energy states of atom (1)

[5]

King Edward VI Five Ways School ""


23/23

44. (a) (i) electrons behave sometimes as particles (1)and sometimes as waves (1)

(ii) mu 18l(or mu = h,l) (1) 3

(b) @or (crystal) diffraction. electron wavelength must be of order ofatom spacing (1)

hence l 1*1m (1)

u= m

h

(1)=131

3"

111.9

1!.!

= 7&(-) # 1m s

1(1) 4

(c) deflection in ,5field(or deflection in 5field. or any other correct evidence) (1) 1

[8]

module 1 - em radiation and quantum ms (2) (1)

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