What is the wavelength of light emitted when the electron in a hydrogen atom undergoes trnsition from an energy level with n = 4 to an energy level with n = 2 ?

Explanation

We are given that `n _(1) = 2, n _(2) = 4`
We are to find out the wavelength of light.
The frequency (v) of the radiations emitted when an electron jumps from a higher orbit `n_(2)` to a lower orbit `n _(1).`
`v = 3.29 xx 10 ^(15) [ (1)/( n _(1) ^(2)) - (1)/( n _(2) ^(2)) ] s ^(-1)`
But `v = (c)/( lamda )`
Hence, `(c)/(lamda ) = 3. 29 xx 1 0 ^(15) [(1)/( n _(1) ^(2) ) - (1)/(n _(2) ^(2)) ]`
`(1)/(lamda ) = ( 3. 29 xx 10 ^(15) )/(c) [ (1)/( n _(1) ^(2)) - (1)/( n _(2) ^(2)) ] = ( 3 .29 xx 10 ^(15))/( 3 xx 10 ^(8) ms ^(-1)) [ (1)/(4) - (1)/(16) ] s ^(-1)`
`= 1. 0 97 xx 10 ^(7) [ (16 - 4)/( 4 xx 16)] m ^(-1) = 2. 0 57 xx 10 ^(6) m ^(-1).`
So, `lamda = (1)/( 2. 0 57 xx 10 ^(6) ) m = 4. 86 xx 10 ^(-7) m`
` = 4. 86 xx 10 ^(-7) xx 10 ^(9) nm = 486 nm.`