A hydrogen atom changes its state from n=3 to n=2. Due to recoil, the percentage change in the wavelength of emitted light is approximately 1 10-n. The value of n is . [Given Rhc=13.6 eV, hc=1242 eV nm, h=6.6 10-34 J s, mass of the hydrogen atom =1.6 10-27 kg]
Answer
7
Solution
Energy released: E=13.6 ( 122- 132 )=13.6 536 1.89 eV
Momentum conservation: atom recoils with p= Ec recoil KE = p22m= E22mc2
photon energy falls by this amount, EE= E2mc2
= 1.89 1.6 10-192 1.6 10-27 (3 108)2
1.05 10-9
% change 1 10-7 n=7
Answer: 7