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Atoms and Nuclei question

2023 · 6 Apr · Shift 1 · Q59
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Atoms and Nuclei question

2023 · 6 Apr · Shift 1 · Q59

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1
The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is : JEE Main 2023 (Online) 6th April Morning Shift Physics - Atoms and Nuclei Question 64 English
  1. A
    A
  2. B
    C
  3. C
    B
  4. D
    D
View written solutionFree

Correct answer: D

  1. For an emitted photon, the wavelength is related to the energy difference by

E=hν=hcλE = h\nu = \frac{hc}{\lambda}E=hν=λhc​

So, shortest wavelength means:

λ∝1ΔE\lambda \propto \frac{1}{\Delta E}λ∝ΔE1​

Hence, we need the transition with the largest energy gap.

  1. In the hydrogen atom, energy levels are given by

En=−13.6n2 eVE_n = -\frac{13.6}{n^2}\,\text{eV}En​=−n213.6​eV

Thus, lower levels are farther apart, and transitions ending at much lower levels generally have greater energy difference.

  1. From the given level diagram, compare the marked transitions A,B,C,A, B, C,A,B,C, and DDD.

The transition labeled D corresponds to the largest drop in energy among the shown transitions.

Therefore, it emits the photon of maximum energy, hence minimum wavelength.

  1. So the transition corresponding to emission of shortest wavelength is:

D\boxed{D}D​

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