Question

The ratio of energies of photons produced due to the transition of an electron of a hydrogen atom from its (i) second to first energy level and (ii) highest energy level to the third level is respectively

Options

• 3 : 2

• 16 : 3

• 27 : 4

• 9 : 4

Answer 1

27 : 4

Explanation:

Let E₁ be the energy of the first energy level,

then E₂ = \[\frac{\mathrm{E}_1}{4}\]

For the highest level E_∞ = 0

∴ \[\mathrm{E}_2-\mathrm{E}_1=\frac{\mathrm{E}_1}{4}-\mathrm{E}_1=-\frac{3}{4}\mathrm{E}_1\]

Similarly, \[\mathrm{E}_3=-\frac{\mathrm{E}_1}{9}\]

\[\mathrm{E}_\infty-\mathrm{E}_3=0-\frac{\mathrm{E}_1}{9}=-\frac{\mathrm{E}_1}{9}\]

∴ \[\frac{\mathrm{E}_{2}-\mathrm{E}_{1}}{\mathrm{E}_{\infty}-\mathrm{E}_{2}}=27:4\]