In hydrogen and hydrogen-like atom , the ratio of `E_(4 n) - E_(2 n) and E_(2 n) - E_(n)` varies with atomic nimber `z` and principal quantum number`n` as

Options

A. `(z^(2))/(n^(2))`
B. `(z^(4))/(n^(4))`
C. `(z)/(n)`
D. none of these

Answer

D

Explanation

`(E_(4 n) - E_(2 n))/ (E_(2 n) - E_(n)) = ((E_(1))/(16 n^(2)) - (E_(1))/(4 n^(2)))/((E_(1))/(4 n^(2)) - (E_(1))/(n^(2))) = (1)/(4) = constant`