Question

H - atom in its ground state is excited by means of monochromatic radiation of wavelength $970.6A^0$ then

• A. The H - atom is excited to 4^th level
• B. Longest wavelength of spectral line when excited atom returns to ground state is 1.875 x 10⁴A⁰
• C. Shortest wavelength of spectral line when excited atom returns to ground state is 1.875 x 10⁴A⁰
• D. The H - atom is excited to 3^rd level.

Answer 1

The correct option is B

Longest wavelength of spectral line when excited atom returns to ground state is 1.875 x 10⁴A⁰

$\Delta E=hv$

= $\frac{6.625\times {10}^{-34}\times 3\times {10}^8}{9.70\times {10}^{-}8}$

= $2.05\times {10}^{18}J$

= $\frac{2.05\times {10}^{18}}{1.6\times {10}^{-19}}ev$

= $12.8ev$

$-\frac{13.6}{n^2}-13.6=12.8$

$n^2=\frac{13.6}{0.8}$

$n^2=16$

$n=4$

$\frac{1}{\lambda }=R[\frac{1}{3^2}-\frac{1}{4^2}]$

$\frac{1}{\lambda }=R\frac{5}{9\times 16}$

$\lambda =\frac{9\times 16}{7R}=\frac{9\times 16}{7}\times 912\AA$

= $1.87\times {10}^4\AA$