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 :
\[-5.447\times {{10}^{-12}}erg\,\,ato{{m}^{-1}}\]
Solution :
If we assume the atom to be hydrogen like, energy of $${n^{th}}$$ energy level
$${E_n} = - \frac{{{E_1}}}{{{n^2}}}$$
where $${{E_1}}$$ is energy of first energy level
$$\eqalign{
& {E_2} = - \frac{{{E_1}}}{{{2^2}}} \cr
& = - \frac{{{E_1}}}{4} \cr
& = \frac{{ - 21.79 \times {{10}^{ - 12}}}}{4} \cr
& = - 5.447 \times {10^{ - 12}}erg\,\,per\,\,atom. \cr} $$