Question

The wave number of the shortest wavelength of absorption spectrum of hydrogen atom is_ _ _ _
(Rydberg constant = \(109700\,\mathrm{cm^{-1}}\)).

Hint:

In absorption spectrum, shortest wavelength corresponds to series limit (highest transition).

Answer 1

Correct Answer: 27425

Concept: Rydberg formula: \[ \bar{\nu} = R \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \]

Step 1:Absorption spectrum Electron absorbs energy and moves from lower to higher level. For absorption (Balmer limit), lowest level involved is: \[ n_1 = 2 \]

Step 2:Shortest wavelength Shortest wavelength \(\Rightarrow\) maximum wave number \[ n_2 = \infty \]

Step 3:Substitute \[ \bar{\nu}_{max} = R \left(\frac{1}{2^2} - \frac{1}{\infty^2}\right) \] \[ = R \left(\frac{1}{4} - 0\right) = \frac{R}{4} \]

Step 4:Final value \[ \bar{\nu}_{max} = \frac{109700}{4} = 27425\,\mathrm{cm^{-1}} \] Conclusion: \(27425\,\mathrm{cm^{-1}}\)