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  4. The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom, is

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Q. The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom, is

Punjab PMETPunjab PMET 2005Atoms

Solution:

Radius of orbit $r_{n} \propto n^{2}$
For first excited state $n=2$
and for ground state, $n=1$
$\therefore \frac{r_{2}}{r_{1}}=\left(\frac{2}{1}\right)^{2}=\frac{4}{1}$
$\therefore $ Ratio of areas $=\left(\frac{r_{2}}{r_{1}}\right)^{2}$
$=\left(\frac{4}{1}\right)^{2}=16: 1$