Question

An X-ray photon of wavelength 0.010 nanometers strikes a helium nucleus and bounces straight back. If the helium nucleus was originally at rest calculate its velocity after interacting with the x-ray.

Answer 1

If the kinetic energy of the incoming X ray is calculated, you can find out the velocity of the helium nucleus. The kinetic energy can be calculated by the equation,
\[K=hf=hc/\lambda \]
i.e., \[K= (6.63*10^{-34})* (3*10^{8})/0.010*10^{-9}\]

When this kinetic energy is equated with \[1/2mv ^{2}\], where m is the mass of the helium nucleus, you can find out the value of v. mass of helium nucles is 4U, i.e., \[4*1.66*10^{-24}\] grams.

Answer 2

You should use conservation of momentum, not kinetic energy.

The wavelength of the X-ray will give you its momentum before and after the collision.

The change in momentum of the X-ray will give you the momentum of the helium nucleus.

Answer 3

Agreed, thats also a very good way to solve the problem. But my process is not wrong is it?

Answer 4

The question doesnt say anything about the velocity of the x-ray photon after collision...so finding the momentum after the collision will be tough.

Answer 5

Velocity is not a problem: a photon always travels at c. The problem is that in order to achieve conservation of energy, the photon's frequency will decrease from f to f'.

If you assume \(f' \approx f \) and apply conservation of momentum, then the equation will be:

\(\dfrac {hf}{c}+0=-\dfrac {hf'}{c}+Mv\)

hence: \(v\approx\dfrac{2h}{M\lambda}\)