Problem D 179

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Atomic Physics

Problem DDE BROGLIE WAVES

P R O B L E MIn 1974, the most massive elementary particle known was the y particle,which has a mass of about four times the mass of a proton. If the deBroglie wavelength is 3.615 1011 m when it has a speed of 2.80 103

m/s, what is the particles mass?

S O L U T I O NGiven: l = 3.615 1011 m v = 2.80 103 m/s

h = 6.63 1034 Js

Unknown: m = ?

Use the equation for the de Broglie wavelength.

m = lh

v = = 6.55 1027 Kg

(6.63 1034 Js)

(3.615 1011 m)(2.80 103 m/s)

ADDITIONAL PRACTICE

1. The worlds smallest watch, made in Switzerland, has a fifteen-jewelmechanism and is less than 5 mm wide. When this watch has a speed of

3.2 m/s, its de Broglie wavelength is 3.0 1032 m. What is the mass of the

watch?

2. Discovered in 1983, Z was still the most massive particle known in 1995.If the de Broglie wavelength of the Z particle is 6.4 1011 m when the

particle has a speed of 64 m/s, what is the particles mass?

3. Although beryllium, Be, is toxic, the Be2+ ion is harmless. When a Be2+

ion is accelerated through a potential difference of 240 V, the ions de

Broglie wavelength is 4.4 1013 m. What is the mass of the Be2+ ion?

4. In 1972, a powder with a particle size of 2.5 nm was produced. At whatspeed should a neutron move to have a de Broglie wavelength of 2.5 nm?

5. The graviton is a hypothetical particle that is believed to be responsiblefor gravitational interactions. Although its existence has not been proven,

cosmological observations and theories indicate that its mass, which is

theoretically zero, has an upper limit of 7.65 1070 kg. What speed must

a graviton have for its de Broglie wavelength to be 5.0 1032 m? (Gravi-

tons are predicted to have a speed equal to that of light.)

6. The average mass of the bee hummingbird is about 1.6 g. What is the deBroglie wavelength of this variety of hummingbird if it is flying at 3.8 m/s?

7. In 1990, Dale Lyons ran 42 195 m, in 3 h, 47 min, while carrying a spoonwith an egg in it. What was Lyons average speed during the run? If the

eggs mass was 0.080 kg, what was its de Broglie wavelength?

Holt Physics Solution ManualII Ch. 216

II

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ht Holt, Rineh

art a

nd Winston

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1

)

1. v = 3.2 m/s

l = 3.0 1032 m

h = 6.63 1034 Js

m = lh

v = =

2. l = 6.4 1011 m

6.9 103 kg6.63 1034 Js

(3.0 1032 m)(3.2 m/s)

Additional Practice D

v = 64 m/s

h = 6.63 1034 J smv =

lh

m = lh

v

m =

m = 1.6 1025 kg

6.63 1034 J s

(6.4 1011 m)(64 m/s)

lc

t

3. q = (2)(1.60 1019 C) =3.20 1019 C

V = 240 V

h = 6.63 1034 J s

l = 4.4 1013 m

KE = qV = 12mv2

m = 2q

V

2V

v = l

h

m = = 1.0 105 m/s

m =

m = 1.5 1026 kg

2(3.20 1019 C)(240 V)

(1.0 105 m/s)2

6.63 1034 J s

(4.4 1013 m)(1.5 1026 kg)

Section TwoProblem Workbook Solutions II Ch. 217

II

Copyrig

ht

Holt, Rineh

art a

nd Winston

.All rights reserved.

4. l = 2.5 nm = 2.5 109 m

mn = 1.675 1027 kg

h = 6.63 1034 J s

mv = lh

v = lm

h

n

v =

v = 1.6 102 m/s

6.63 1034 J s

(2.5 109 m)(1.675 1027 kg)

Givens Solutions

5. m = 7.65 1070 kg

l = 5.0 1032 m

h = 6.63 1034 J s

mv = lh

v = lh

m

v =

v = 1.7 103 m/s

6.63 1034 J s

(5.0 1032 m)(7.65 1070 kg)

6. m = 1.6 g = 1.6 103 kg

v = 3.8 m/s

h = 6.63 1034 J s

mv = lh

l = m

h

v

l =

l = 1.1 1031 m

6.63 1034 J s

(1.6 103 kg)(3.8 m/s)

7. x = 42 195 m

t = 3 h 47 min = 227 min

m = 0.080 kg

h = 6.63 1034 J s

v =

x

t = =

lh = mv

l = m

h

v

l =

l = 2.7 1033 m

6.63 1034 J s

(0.080 kg)(3.10 m/s)

3.10 m/s42 195 m

(227 min)16m0 isn

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