The diagram shows four energy . . .

Question : The diagram shows four energy levels of an electron in Bohr model of hydrogen atom. Identify the transition in which emitted photon will have longest wavelength : 

(a) I 
(b) II
(c) III
(d) IV

Doubt by Faisal 

Solution : 

We know, 
E1=-13.6 eV
E2=-3.4 eV
E3=-1.51 eV
E4=-0.85 eV

For First Transition 
E4-E3
=-0.85-(-1.51)
=-0.85+1.51
=0.66 eV

For II Transition 
E3-E1
=-1.51-(-13.6)
=-1.51+13.6
=12.09 eV

For III Transition 
E2-E1
=-3.4-(-13.6)
=-3.4+13.6
=10.2 eV

For IV Transition 
E3-E2
=-1.51-(-3.4)
=-1.51+3.4
=1.89 eV

EII(12.09 eV)>EIII(10.2 eV)>EIV (1.89 eV)>EI(0.66 eV)

Also, we know that
E=hc/
λ
E∝1/λ
I transition will have the longest wavelength. 

Hence, (a) I, would be the correct option.