Question

A hydrogen atom is in an excited state of principle quantum number n. It emits a photon of wavelength l when returns to the ground state. The value of n is –

• A. $\sqrt{\lambda R(R - 1)}$
• B. $\sqrt{\frac{\lambda R}{\lambda R - 1}}$
• C. $\sqrt{\frac{(\lambda R - 1)}{\lambda R}}$
• D. $\sqrt{\lambda(R–1)}$

Answer 1

Answer: (B)

$\sqrt{\frac{\lambda R}{\lambda R - 1}}$

Answer 2

$\frac{1}{\lambda}$= R $\left\lbrack \frac{1}{1} - \frac{1}{n^{2}} \right\rbrack$

$\frac{1}{n^{2}}$ = $1 - \frac{1}{\lambda R}$

n = $\sqrt{\frac{\lambda R}{\lambda R - 1}}$