Student Solutions Manual With Study Guide, Volume 2 For Serway/vuilles College Physics, 10th
Student Solutions Manual With Study Guide, Volume 2 For Serway/vuilles College Physics, 10th
10th Edition
ISBN: 9781285866260
Author: SERWAY
Publisher: CENGAGE L
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Question
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Chapter 28, Problem 28P

(a)

To determine

The expression for the energy level of the sole remaining electron.

(a)

Expert Solution
Check Mark

Answer to Problem 28P

The expression for the energy level of the sole remaining electron is En=(122eV)n2.

Explanation of Solution

Formula to calculate the energy level is,

  En=Z2(13.6eV)n2

  • En is the nth energy level,
  • n is nth level
  • Z is the atomic number

Substitute 3 for Z to find En.

  En=(3)2(13.6eV)n2=(122eV)n2

Thus, expression for the energy level is (122eV)n2.

Conclusion:

Therefore, the expression for the energy level is (122eV)n2.

(b)

To determine

The energy for the level n=4.

(b)

Expert Solution
Check Mark

Answer to Problem 28P

The energy for the level n=4 is 7.63eV.

Explanation of Solution

Formula to calculate the energy level is,

  En=(122eV)n2

  • En is the nth energy level,
  • n is nth level

Substitute 4 for n to find En.

  E4=(122eV)(4)2=7.63eV

Thus, the energy for the level n=4 is 7.63eV.

Conclusion:

Therefore, the energy for the level n=4 is 7.63eV.

(c)

To determine

The energy for the level n=2.

(c)

Expert Solution
Check Mark

Answer to Problem 28P

The energy for the level n=2 is 30.5eV.

Explanation of Solution

Formula to calculate the energy level is,

  En=(122eV)n2

  • En is the nth energy level,
  • n is nth level

Substitute 2 for n to find En.

  E2=(122eV)(2)2=30.5eV

Thus, the energy for the level n=2 is 30.5eV.

Conclusion:

Therefore, the energy for the level n=2 is 30.5eV.

(d)

To determine

The energy of the photon for the transition from fourth level to second level.

(d)

Expert Solution
Check Mark

Answer to Problem 28P

the energy of the photon for the transition from fourth level to second level is 22.9eV or 3.66×1018J.

Explanation of Solution

Formula to calculate the energy difference is,

  Ephoton=(E4E2)

  • E2andE4 are the second and fourth level energy,
  • En is nth level energy

From unit conversion,

    1eV=1.6×1019J

Substitute (7.63eV) for E4, (30.5eV) for E2 to find Ephoton.

  Ephoton=[(7.63eV)(30.5eV)]=22.9eV=22.9eV×1.6×1019J1eV=3.66×1018J

Thus, the energy of the photon for the transition from fourth level to second level is 22.9eV or

3.66×1018J.

Conclusion:

Therefore, the energy of the photon for the transition from fourth level to second level is 22.9eV or 3.66×1018J.

(e)

To determine

The frequency and wavelength of the emitted photon.

(e)

Expert Solution
Check Mark

Answer to Problem 28P

The frequency and wavelength of the emitted photon is 5.52×1015Hz and 5.43×108m respectively.

Explanation of Solution

Formula to calculate the frequency of the photon is,

  f=Ephotonh

  • Ephoton is the photon energy
  • h is Planck’s constant

Substitute 3.66×1018J for Ephoton, 6.63×1034J-s for h to find f.

  f=(3.66×1018J)(6.63×1034J-s)=5.52×1015Hz

Formula to calculate the wavelength of the photon is,

  λ=cf

  • c is the speed of light
  • f is the frequency

Substitute 3×108m/s for c, 5.52×1015Hz for f to find λ.

  λ=3×108m/s5.52×1015Hz=5.43×108m

Thus, the frequency and wavelength of the emitted photon is 5.52×1015Hz and 5.43×108m respectively.

Conclusion:

Therefore, the frequency and wavelength of the emitted photon is 5.52×1015Hz and 5.43×108m respectively.

(f)

To determine

The wavelength belongs to in which spectrum.

(f)

Expert Solution
Check Mark

Answer to Problem 28P

The wavelength belongs to in which spectrum is deep ultraviolet region.

Explanation of Solution

The wavelength of the photon for the transition is 5.43×108m. So, this wavelength belongs to deep ultraviolet region.

Thus, this wavelength belongs to deep ultraviolet region.

Conclusion:

Therefore, the wavelength belongs to deep ultraviolet region

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