Atomic StructureHard

Question

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

Options

A.2: 1
B.4: 1
C.8: 1
D.16: 1

Solution

$\frac{A_{2}}{A_{1}} = \frac{\left( \pi r^{2} \right)_{2}}{\left( \pi r^{2} \right)_{1}} = \left( \frac{r_{2}}{r_{1}} \right)^{2} = \left( \frac{r_{1} \times 2^{2}}{r_{1}} \right)^{2} = \frac{16}{1}$

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