A hydrogen-like atom emits rediationof frequency `2.7 xx 10^(15)` Hz` when if makes a transition from `n = 2 to n = 1`. The frequency emitted in a transition from `n = 3 to n = 1` will be

Options

A. `1.8xx10^(15)` Hz
B. `3.2xx10^(15)` Hz
C. `4.7xx10^(15)` Hz
D. `6.9xx10^(15)` Hz

Answer

B

Explanation

Accroding to Bohr's theroy, the wavelength of the `(1)/(lambda)=Z^(2)R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))rArr(v)/(c)=Z^(2)R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`v=cZ^(2)((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) rArr2.7xx10^(15)=cZ^(2)((1)/(1^(2))-(1)/(2^(2)))`
`v=cZ^(2)R((1)/(1^(2))-(1)/(3^(3)))rArrv=(32)/(27)xx2.710^(15)`
`=3.2xx10^(15)Hz`