Question

A proton with kinetic energy, K strikes another proton at rest. If the collision is head – on, find the correct graph between K and the distance of closest approach, r.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

At closest approach, both protons will be moving with same velocity.

Applying Conservation of momentum for the system,

$m{v}_0=2mv$

$\Delta KE=\frac{1}{2}m{v}_0^2-2.\frac{1}{2}m(\frac{v_2}{2}{)}^2=\frac{e^2}{4\pi {\epsilon }_{0}r}$

$\frac{1}{4}m{v}_0^2=\frac{e^2}{4\pi {\epsilon }_{0}r}$

$or,Kr=\frac{e^2}{2\pi {\epsilon }_0}=constant$

which implies that , $K\propto \frac{1}{r}$ (here K is kinetic energy of incident particle)