A 12.9 eV beam of electrons is used to bombard gaseous hydrogen atom at room temperature. Upto which energy level the hydrogen atoms would be excited?
Calculate the wavelength of the first member of Paschen series and first member of Balmer series.

Explanation

Ground state energy of gaseous hydrogen at room temp. =-13.6eV.
On bombardment, total energy
`=-13.6+12.9=-0.7eV`
`-13.6/(n^2)=-0.7eV :. n^2=13.6/0.7 =19.4`
`n=sqrt19.4=4.4lt5`
`:.` Electron is excited to n=4, i.e., 4th energy level.
for first member of Paschen series,
`n_1=3, n_2=4`
`hv=(hc)/lambda=E_4-E_3=-13.6/(4^2)-(-13.6/(3^2))`
`=-0.85+1.51=0.66eV`
`lambda=(hc)/(0.66xx1.6xx10^(-19))=(6.6xx10^(-34)xx3xx10^8)/(0.66xx1.6xx10^(-19))`
`=18.75xx10^-7m`
for first member of Balmer series,
`n_1=2, n_2=3`.
`hv=(hc)/lambda=E_3-E_2=-13.6/(3^2)-(-13.6/(2^2))`
`=-1.51+3.4=1.89eV`
`lambda=(hc)/(1.89xx1.6xx10^(-19))=6.547xx10^-7m`