Question

An electron in hydrogen is in the 3d state.

What are the allowed transition(s) if the electron moves to a higher energy state(s) (the photon carries one unit of angular momentum)?

Answer 1

We know that

the energy in hydrogen atom is  

En = -13.6 /n^2 eV

for the electron in the third state then the energy is  

E3 = -13.6 /3^2 = -1.511 eV

E2 = -13.6 /2^2 = - 3.4eV

E1 = -13.6/1^2 = -13.6 eV

when the electron is making transitionfrom 3 to 2 the energy difference is

E2-E3 = 3.4-1.511 eV = 1.889 eV = 3.0224*10^-19 J corresponding wavelenght is

E = h*c/lambda ==> lambda = h*c/E

Lambda = 6.625*10^-34*3*10^8/(3.0224*10^-19) m

Lambda = 6.5759*10^-7 m = 657.59 nm

from E3 to E1  

13.6-1.511 eV = 12.089 eV = 1.93424*10^-18 J

E = h*c/lambda ==> lambda = h*c/E

Lambda = 6.625*10^-34*3*10^8/(1.93424*10^-18) m

Lambda = 1.027535*10^-7 m = 102.7535 nm

from E2to E1

13.6-3.4 eV = 10.2 eV = 16.32*10^-19 J

E = h*c/lambda ==> lambda = h*c/E

Lambda = 6.625*10^-34*3*10^8/(16.32*10^-19) m

Lambda = 1.217831*10^-7 m = 121.7831 nm

so these are allowed transitions