The ratio of the areas of the orbit for the second excited state to the first excited state for the hydrogen atom is

Options

A. `2:1`
B. `9/4`
C. `81/16`
D. `16/81`

Answer

C

Explanation

For first excited state n=2
For second excited state n=3
`r prop n^2 " and " A = pi r^2 therefore A prop n^4`
`therefore A_3/A_2 = 3^4/2^4 = 81 /16`