Question

The energy of electron in first energy level is $-21.79\times {10}^{-12}$ erg per atom. The energy of electron in second energy level is :

• A. $-54.47\times {10}^{-12}$ erg $ato{m}^{-1}$
• B. $-5.447\times {10}^{-12}$ erg $ato{m}^{-1}$
• C. $-0.5447\times {10}^{-12}$ erg $ato{m}^{-1}$
• D. $-0.05447\times {10}^{-12}$ erg $ato{m}^{-1}$

Answer 1

The correct option is B $-5.447\times {10}^{-12}$ erg $ato{m}^{-1}$

For a particular element,
$E_n=\frac{13.6Z^2}{n^2}erg$ $at{m}^{-1}$
$\therefore E_n\propto \frac{1}{n^2}$
$\therefore \frac{E_1}{E_2}=\frac{\left(n_2^2\right)}{(n_1{)}^2}$
or, $E_2=\frac{(1{)}^2\times (-21.79\times {10}^{-12})}{(2{)}^2}$
$=-5.447\times {10}^{-12}$ erg $at{m}^{-1}$