A hydrogen atom moves with a velocity u and makes a head on inelastic collision with another stationary hydrogen atom. Both are in the ground state before collision. What is the minimum value of u (in x104 m/s ), 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 x 1.66 x 10-27 kg.

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answer is 0006.24.

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Detailed Solution

From conservation of momentum mu=2mv⇒ v=u/2..........(i) The energy of excitation ΔE is given by ΔE=12mu2−2×12m(u/2)2⇒ ΔE=14mu2.......(ii)The minimum excitation energy for a H-atom is for transition n1 = 1 to n2 = 2 which corresponds to an energy of 10.2 eVFrom Eq. (2)14×1.0078×1.66×10−27u2=10.2×1.6×10−19⇒u=6.24×104m/s

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