A hydrogen atom moves with a velocity u, and makes a head on inelastic collision are in the ground state before collision. What is the minimum value of u, if one of them is to be given a minimum excitation energy? The ionization energy is 13.6 eV. Mass of the hydrogen atom is 1.0078 × 1.66 × 10 –27 kg.
Text Solution
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Sol. From conservation of momentum
Mu = 2mv or v = u/2 … (1)
The energy of excitation Δ E is given by
Δ E = 
mu 2 – 2 × 
m(u/2) 2 = 
mu 2 … (2)
The minimum excitation energy for a H-atom is for transition n 1 = 1 to n 2 = 2 which corresponds to an energy of 10.2 eV.
From equation-(2)
× (1.0078 × 1.66 × 10 –27 )u 2 = 10.2 × (1.6 × 10 –19 )
u = 6.24 × 10 4 m/s.
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