Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Question
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Chapter 28, Problem 64P

(a)

To determine

The energy difference between the first excited state and the ground state.

(a)

Expert Solution
Check Mark

Answer to Problem 64P

The energy difference is 6 MeV.

Explanation of Solution

The length of the box is 1014m.

Write the expression for energy of the quantized level.

E1=h28mL2                                                           (I)

Here, E1 is the ground state energy, h is the Planck’s constant, m is the mass and L is the length of the box.

Write the expression for energy of the quantized level in terms of the ground state energy.

En=n2E1                                                           (II)

Here, En is the energy of the level n, n is the quantum number and E1 is the energy of the ground state.

Substituting 2 for n in (II)

E2=22E1                                                           (III)

Here, E2 is the energy of the first excited state.

Write the expression for energy difference between the first excited state and the ground state.

ΔE=E2E1                                                          (IV)

Here, ΔE is the energy difference.

Substituting (III) in (IV)

ΔE=22E1E1=3E1                                                          (V)

Substituting (I) in (V)

ΔE=3h28mL2                                                           (VI)

Substituting 6.626×1034 Js for h, 1.673×1027kg for m and 0.20 eV for  L in (VI) to find ΔE

ΔE=3×(6.626×1034 Js)28×1.673×1027kg×(1014m)2×1 eV1.602×1019J=6 MeV

Thus, the energy difference is 6 MeV.

(b)

To determine

The wavelength and frequency of the emitted photon.

(b)

Expert Solution
Check Mark

Answer to Problem 64P

The wavelength of the emitted photon is 0.2 pm, its frequency is 1.5×1021 Hz and it belongs to the gamma ray of the electromagnetic spectrum.

Explanation of Solution

Write the expression for the energy of a photon.

E=hcλ                                                           (VII)

Here, λ is the wavelength, h is the Planck’s constant, c is the velocity of light and E is the energy of the photon.

Rearranging (I)

λ=hcE                                                           (VIII)

Write the expression for frequency.

ν=cλ                                                          (IX)

 Here, ν is the frequency of the photon.

Substitute 6.626×1034 Js for h, 3×108 ms1 for c and  6 MeV for E in (VIII) to find λ

λ=6.626×1034 Js×3×108 ms16 MeV=6.626×1034 Js×3×108 ms16×106 eV×1 eV1.602×1019 J=0.2×1012 m=0.2 pm

Thus, the wavelength of the photon is 0.2 pm.

Substitute 3×108 ms1 for c and  0.2 pm for λ in (IX) to find ν.

ν=3×108 ms10.2×1012 m=1.5×1021 Hz

Thus, the wavelength of the photon is 1.5×1021 Hz.

This wavelength and frequency corresponds to the gamma ray of the electromagnetic spectrum.

(c)

To determine

The plot of the wave function of the electron in the ground state and first three excited states.

(c)

Expert Solution
Check Mark

Answer to Problem 64P

The wave function is a sine wave.

Explanation of Solution

The length of the box is 1014m i.e. 10fm.

Write the expression for the wave function of a particle in a box.

ψn=2Lsin(nπxL)                                                     (X)

Here, ψn is the wave function of the quantum state n, L is the length of the box  and x is the position co-ordinate.

Substitute 1,2,3and 4 for n in (VIII) to find their corresponding wavefunctions ψ1,ψ2,ψ3and ψ4 respectively.

ψ1=210 fmsin(πx10 fm)                                                    (XI)

ψ2=210 fmsin(2πx10 fm)                                                   (XII)

ψ3=210 fmsin(3πx10 fm)                                                   (XIII)

ψ4=210 fmsin(4πx10 fm)                                                   (XIV)

The plot of the wave function versus position is given below:

Physics, Chapter 28, Problem 64P , additional homework tip  1

Physics, Chapter 28, Problem 64P , additional homework tip  2

Physics, Chapter 28, Problem 64P , additional homework tip  3

Physics, Chapter 28, Problem 64P , additional homework tip  4

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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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