PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Question
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Chapter 28, Problem 50P

(a)

To determine

The quantum number of the marble.

(a)

Expert Solution
Check Mark

Answer to Problem 50P

The quantum number of the marble is 6×1028.

Explanation of Solution

The mass of the marble is 10 g, its speed is 2cms1 and the length of the box is 10 cm.

Write the expression for momentum of a particle in a box.

pn=nh2L                                                            (I)

Here, pn is the momentum of the marble, n is the quantum number, h is the Planck’s constant and L is the length of the box.

Rearranging (I) for n

n=2pnLh                                                            (II)

Write the classical expression for momentum.

pn=mv                                                           (III)

Here, m is the mass of the marble and v is its speed.

Substituting (III) in (II)

n=2mvLh                                                            (IV)

Substituting 10 g for m, 2cms1 for v, 6.626×1034 Js for h and 10 cm for L in (IV) to find n

n=2×10 g×2cms1×6.626×1034 kgm2s110 cm=2×10×103 kg×2cms1×6.626×1034 kgm2s110 cm=6×1028

Thus, the quantum number of the marble is 6×1028.

(b)

To determine

The reason why the quantization of the marble isn’t observable.

(b)

Expert Solution
Check Mark

Answer to Problem 50P

Because of the small energy difference between two quantized levels of the marble, the quantization isn’t observable.

Explanation of Solution

Write the expression for energy of the quantized level.

En=n2h28mL2                                                            (V)

Here, En is the energy of the level n

Substituting n+1 for n in (I)

En+1=(n+1)2h28mL2                                                            (VI)

Here, En+1 is the energy of the level n+1

Subtracting (I) from (II)

ΔE=(n+1)2h28mL2n2h28mL2ΔE=h28mL2[(n+1)2n2]

Here, ΔE is the energy difference.

Thus, the energy difference is

ΔE=h28mL2(2n+1)                                                           (VII)

Substituting 10 g for m, 2cms1 for v, 6.626×1034 Js for h, 10 cm for L, 6×1028 for n in (VII) to find ΔE

 ΔE=(2(6×1028)+1)×(6.626×1034 Js)28×10 g×(10 cm)2=(12×1028+1)×(6.626×1034 Js)28×10×103 g×(10×102 cm)2=7×1935 J

The energy difference is 7×1935 J which is very small. Thus, they cannot be observed.

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Chapter 28 Solutions

PHYSICS

Ch. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQCh. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQCh. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 16CQCh. 28 - Prob. 17CQCh. 28 - Prob. 18CQCh. 28 - Prob. 1MCQCh. 28 - Prob. 2MCQCh. 28 - Prob. 3MCQCh. 28 - Prob. 4MCQCh. 28 - Prob. 5MCQCh. 28 - Prob. 6MCQCh. 28 - Prob. 7MCQCh. 28 - Prob. 8MCQCh. 28 - Prob. 9MCQCh. 28 - Prob. 10MCQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 15PCh. 28 - Prob. 14PCh. 28 - Prob. 17PCh. 28 - Prob. 16PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 23PCh. 28 - Prob. 22PCh. 28 - Prob. 25PCh. 28 - Prob. 24PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 32PCh. 28 - Prob. 31PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 39PCh. 28 - Prob. 41PCh. 28 - Prob. 40PCh. 28 - Prob. 38PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49PCh. 28 - Prob. 50PCh. 28 - Prob. 51PCh. 28 - Prob. 52PCh. 28 - Prob. 53PCh. 28 - Prob. 54PCh. 28 - Prob. 55PCh. 28 - Prob. 56PCh. 28 - Prob. 57PCh. 28 - Prob. 58PCh. 28 - Prob. 59PCh. 28 - Prob. 60PCh. 28 - Prob. 61PCh. 28 - Prob. 62PCh. 28 - Prob. 63PCh. 28 - Prob. 65PCh. 28 - Prob. 64PCh. 28 - Prob. 66PCh. 28 - Prob. 67PCh. 28 - Prob. 68PCh. 28 - Prob. 69PCh. 28 - Prob. 70PCh. 28 - Prob. 71PCh. 28 - Prob. 72PCh. 28 - Prob. 73PCh. 28 - Prob. 74PCh. 28 - Prob. 75PCh. 28 - Prob. 76PCh. 28 - Prob. 77PCh. 28 - Prob. 79PCh. 28 - Prob. 78PCh. 28 - Prob. 80PCh. 28 - Prob. 81PCh. 28 - Prob. 82PCh. 28 - Prob. 83PCh. 28 - Prob. 84P
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