A hydrogen atom is in an excited state of principal quantaum number$\; (n)\;$ it emits a photon of wavelength $\;(\lambda)\;,$ when it returns to ground state . The value of n is

$(a)\;\sqrt{\large\frac{\lambda R}{\lambda R-1}}\qquad(b)\;\sqrt{\large\frac{(\lambda R-1)}{\lambda R}}\qquad(c)\;\sqrt{\lambda(R-1)}\qquad(d)\;\sqrt{\large\frac{\lambda R}{\lambda R-1}}$

Answer : (d) $\;\sqrt{\large\frac{\lambda R}{\lambda R-1}}$
Explanation :
As $\; \large\frac{1}{\lambda}=R\;(\large\frac{1}{n_{1}^2}-\large\frac{1}{n_{2}^2})$
$\large\frac{1}{\lambda}=R\;(\large\frac{1}{1^2}-\large\frac{1}{n^2})$
$\large\frac{1}{\lambda R}=1-\large\frac{1}{n^2} \quad \; or \qquad \large\frac{1}{n^2}=1-\large\frac{1}{\lambda R}=\large\frac{\lambda R-1}{\lambda R}$
$n=\sqrt{\large\frac{\lambda R}{\lambda R-1}}\;.$
answered Feb 24, 2014 by