The ground state energy of hydrogen atom is -13.6 eV . If an electron makes a transition from an energy level -0.85 eV to -3.4 eV, calculate the wavelength of the spectral line emitted . To which series of hydrogen spectrum does this wavelength belong ?

Explanation

Given , `E_1 =-13.6 eV.`
Now , `(-13.6)/(-0.85) =16 and (-13.6)/(-3.4)=4`
As `E prop 1/(n^2),` the two given levels correspond to n =4 and n=2 , respectively.
The spectral line emitted due to `4 to 2` transition belongs to the Balmer series.
Photon energy due to this transition is,
`hf=(hc)/(lambda) =-0.85-(-3.4)=2.55eV`
`therefore lambda =(hc)/(2.55eV)=((6.626xx10^(-34))xx(3xx10^8))/(2.55xx1.6xx10^(-9))m`
`=((6.626xx10^(-34))xx(3xx10^8))/(2.55xx1.6xx10^(-19))xx10^(10)"Å"=4872 "Å"`