A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy. Level the hydrogen atoms would be excited ? Calculate the wavelengths of the first memeber of Lyman and first member of Balmer series.

Explanation

For Hydrogen atom
The 1st excited energy =`E_2-E_1`=10.2 eV
The 2nd excited energy =`E_3-E_1` =12.09 eV
The 3rd excited energy = `E_4-E_1`=12.75 eV
Hence hydrogen atoms will be excited to 4th energy level or 3rd excited state.
For Balmer series
`1/lambda=R(1/2^2-1/3^2)`
`1/lambda=Rxx5/36`
`lambda=36/(5R) =36/(5xx1.09xx10^7)`
`=6.605xx10^(-7)` m
For Lyman series
`1/lambda=R(1/1^2-1/2^2)=1.097xx10^7xx3/4`
`lambda=4/(3xx1.097xx10^7)`
`=1.215xx10^(-7)` m