If `lamda_(1)` and `lamda_(2)` denote the wavelengths of de-Broglie waves for electrons in the first and second Bohr orbits in hydrogen atom, then `(lamda_(1))/(lamda_(2))` is equal to :

Options

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

Answer

B

Explanation

In case of first Bohar orbit n=1.
`E_(1)=-13*6eV`
For Bohar.s second orbit n=2
`E_(2)-(13*6)/(2^(2))=(-13*6)/(4)eV`
As `E=(hc)/(lambda)rArr Eprop (1)/(lambda)`
`:. (lambda_(1))/(lambda_(2))= sqrt((E_(2))/(E_(1)))= sqrt((1)/(4))=(1)/(2)`