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The electronic energy levels in a hydrogen atom are given by by En = - 13.6/n2 eV. If a selective excitation to the n = 50 level is to be made using a laser, the maximum allowed frequency line - width of the laser is
  • a)
    0.96 GHz
  • b)
    0.53 GHz
  • c)
    1.6 GHz
  • d)
    16 GHz
Correct answer is option 'B'. Can you explain this answer?
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The electronic energy levels in a hydrogen atom are given by by En = -...












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The electronic energy levels in a hydrogen atom are given by by En = -...
Given:
Electronic energy levels in a hydrogen atom: En = -13.6/n^2 eV
Selective excitation level: n = 50

To find:
Maximum allowed frequency line-width of the laser

Formula:
The frequency of a photon is given by the equation:
E = hf
where E is the energy of the photon, h is the Planck constant (6.63 × 10^-34 J s), and f is the frequency of the photon.

Approach:
1. Calculate the energy difference between the n = 50 level and the ground state (n = 1).
2. Convert the energy difference into electron volts (eV).
3. Use the formula E = hf to find the frequency.
4. Convert the frequency to gigahertz (GHz) by dividing by 10^9.

Calculation:
1. Energy difference:
ΔE = E50 - E1
= (-13.6/50^2) - (-13.6/1^2)
= -0.0272 - (-13.6)
= 13.5728 eV

2. Convert energy difference to joules:
1 eV = 1.6 × 10^-19 J
ΔE_joules = 13.5728 eV × 1.6 × 10^-19 J
= 2.171648 × 10^-18 J

3. Calculate the frequency:
E = hf
f = E/h
= (2.171648 × 10^-18 J)/(6.63 × 10^-34 J s)
≈ 3.279 × 10^15 Hz

4. Convert the frequency to GHz:
1 GHz = 10^9 Hz
f_GHz = (3.279 × 10^15 Hz)/(10^9 Hz/GHz)
= 3.279 GHz

Therefore, the maximum allowed frequency line-width of the laser is 3.279 GHz.

The correct answer is option B: 0.53 GHz. There seems to be an error in the provided answer.
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The electronic energy levels in a hydrogen atom are given by by En = - 13.6/n2 eV. If a selective excitation to the n = 50 level is to be made using a laser, the maximum allowed frequency line - width of the laser isa)0.96 GHzb)0.53 GHzc)1.6 GHzd)16 GHzCorrect answer is option 'B'. Can you explain this answer?
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The electronic energy levels in a hydrogen atom are given by by En = - 13.6/n2 eV. If a selective excitation to the n = 50 level is to be made using a laser, the maximum allowed frequency line - width of the laser isa)0.96 GHzb)0.53 GHzc)1.6 GHzd)16 GHzCorrect answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The electronic energy levels in a hydrogen atom are given by by En = - 13.6/n2 eV. If a selective excitation to the n = 50 level is to be made using a laser, the maximum allowed frequency line - width of the laser isa)0.96 GHzb)0.53 GHzc)1.6 GHzd)16 GHzCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The electronic energy levels in a hydrogen atom are given by by En = - 13.6/n2 eV. If a selective excitation to the n = 50 level is to be made using a laser, the maximum allowed frequency line - width of the laser isa)0.96 GHzb)0.53 GHzc)1.6 GHzd)16 GHzCorrect answer is option 'B'. Can you explain this answer?.
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