JEE Physics 2023 Question with Solution

Given: The question asks which transition gives emission of the shortest wavelength.

Find: The transition with the maximum energy gap.

For an emitted photon,

$$\Delta E = \frac{hc}{\lambda}$$

So,

$$\lambda \propto \frac{1}{\Delta E}$$

For the shortest wavelength, the energy gap must be maximum.

From the given transitions, the correct choice is the transition from $n = 3$ to $n = 1$.

Therefore, the correct option is B.

Given: The energy of a photon emitted during a transition is related to its wavelength.

Find: Which transition corresponds to the shortest wavelength.

The emitted photon satisfies

$$E = \frac{hc}{\lambda}$$

where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength.

For the shortest wavelength, the emitted energy must be maximum.

Also, for a transition,

$$E = E_{\text{initial}} - E_{\text{final}}$$

So the transition with the largest energy difference gives the shortest wavelength.

The hydrogen atom energy levels are given by

$$E_n = -\frac{13.6 \, \text{eV}}{n^2}$$

The solution text indicates that the largest energy difference corresponds to the transition from $n = 3$ to $n = 1$.

Therefore, the transition corresponding to the shortest wavelength is D, which is Option 2, so the correct option label is B.