Question
An electron with kinetic energy $E$ collides with a hydrogen atom in the ground state. The collision will be elastic

Answer

$(b)$ First excitation energy of a hydrogen atom in ground state is $10.2 \,eV$.

So, if energy of colliding electron is more than $10.2 \,eV$, then hydrogen atom absorbs $10.2 \,eV$ from kinetic energy of electron and collision will be inclastic.

If energy of electron is less than $10.2 \,eV$, then hydrogen atom does not absorbs energy and total energy before and after collision remains same and collision will be elastic.

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