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
E1=-13.6 eV
E2=-3.4 eV
E3=-1.51 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
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
=-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
=-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
=-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
E=hc/λ
E∝1/λ
I transition will have the longest wavelength.
Hence, (a) I, would be the correct option.