If `lamda_1` and `lamda_2` denote the wavelength of de Broglie waves for electrons in the first and second Bohr orbits in a hydrogen atom, the `(lamda_1)/(lamda_2)` is equal to

Options

A. `(2)/(1)`
B. `(1)/(2)`
C. `(1)/(4)`
D. `(4)/(1)`

Answer

B

Explanation

Energy of electron nth orbit, `E_n=-(13.6)/(n^2)eV`
for first Bohr orbit, `n=1`
`E_1=-13.6eV`
For second Bohr orbit, `n=2`
`E_2=-(13.6)/(4)eV` or `(lamda_1)/(lamda_2)=sqrt((E_2)/(E_1))`
`(lamda_1)/(lamda_2)=sqrt((1)/(4))implies(lamda_1)/(lamda_2)=(1)/(2)`