Question

An electron collides with a free molecule initially in its ground state. The collision leaves the molecule in an excited state that is metastable and does not decay to the ground state by radiation. Let $K$ be the sum of the initial kinetic energies of the electron and the molecule, the $\overrightarrow{P}$ the sum of their initial momenta. Let $K^{\prime }$ and $\overrightarrow{P}$, represent the same physical quantities after the collision. Then.

• A. $K=K^{\prime },\overrightarrow{P}=\overrightarrow{P^{\prime }}$
• B. $K^{\prime }<K,\overrightarrow{P}=\overrightarrow{P^{\prime }}$
• C. $K=K^{\prime },\overrightarrow{P}\ne \overrightarrow{P^{\prime }}$
• D. $K^{\prime }\ne K,\overrightarrow{P}\ne \overrightarrow{P^{\prime }}$

Answer 1

Answer: (B)

$K^{\prime }<K,\overrightarrow{P}=\overrightarrow{P^{\prime }}$

We shall apply the Principle of conservation of energy and the principle of conservation of momentum to the system of electron and the molecule.

By applying the conservation of momentum rule, which states, under no action of external forces, the momentum of a system remains same.

For the electron-molecule system, net external force = 0.

Thus, final momentum = initial momentum i.e., $\overrightarrow{P^{\prime }}=\overrightarrow{P}$

Similarly, as the external work on the system = 0, and energy input = 0, by the conservation of Energy principle, Total energy of the system is conserved.

However, some part of kinetic energy is used to excite the molecule from ground state to the metastable state. Thus there is an increase in potential energy $\Rightarrow$ there is a decrease in kinetic energy i.e., $K^{\prime }<K$