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Q. The ratio of area covered by second orbital to the first orbital is :

AFMCAFMC 2004

Solution:

According to Bohr
$r_{n} \propto \frac{n^{2}}{Z}\left[r=\frac{0.529 n^{2}}{Z} \,\, \mathring{A}\right]$
$\frac{r_{2}}{r_{1}}=\frac{(2)^{2}}{(1)^{2}}=\frac{4}{1}$
Area $=\pi r^{2}$
$\Rightarrow \frac{A_{2}}{A_{1}}=\frac{\pi r_{2}^{2}}{\pi r_{1}^{2}}=\left(\frac{r_{2}}{r_{1}}\right)^{2}=\left(\frac{4}{1}\right)^{2}=\frac{16}{1}$