JEEOlympiad
An electron with kinetic energy 12.5 eV makes a single head-on…
Question
An electron with kinetic energy 12.5 eV makes a single head-on inelastic collision with a hydrogen atom in its ground state, exciting the atom to the highest level energetically allowed. (Use 13.6 eV for the hydrogen ground-state energy.) After the collision the electron retains some kinetic energy K eV. Compute the integer value of 90*K.
✓ Verified answer: 37checked by our engine — not a guess
Step-by-step solution
The excitation energy from the ground state to level n is 13.6*(1 - 1/n^2).
The highest level the 12.5 eV electron can reach satisfies 13.6*(1 - 1/n^2) <= 12.5.
For n=3: 13.6*(1 - 1/9) = 13.6*8/9 = 12.0889 eV <= 12.5 (allowed).
For n=4: 13.6*(1 - 1/16) = 12.75 eV > 12.5 (not allowed).
So the atom is excited to n=3, absorbing 544/45 eV.
The electron retains K = 12.5 - 544/45 = 562.5/45 - 544/45 = 18.5/45 = 37/90 eV.
Therefore 90*K = 37.
Final answer37
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