Question

Find the momentum of a (100 {keV}) x-ray photon.

a) (3.98 times 10⁻²³ {kg}cdot{m/s})
b) (5.02 times 10⁻²³ {kg}cdot{m/s})
c) (6.31 times 10⁻²³ {kg}cdot{m/s})
d) (7.96 times 10⁻²³ {kg}cdot{m/s})

Answer 1

b) The momentum of the 100 keV x-ray photon is
`\(5.02 * 10^(-23) \, \text{kg} \cdot \text{m/s}\)`. This is calculated using the equation
`\(p = (E)/(c)\)` with (E) as the energy of the photon and (c) as the speed of light.

Step-by-step explanation:

To find the momentum of a photon, you can use the equation
`\( p = (E)/(c) \)`, where ( p ) is the momentum, ( E ) is the energy of the photon, and ( c ) is the speed of light. Given the energy of the x-ray photon as 100 keV, convert it to joules (1 eV = 1.602 x 10⁻¹⁹ J) to get ( E = 1.602 x 10⁻¹⁶ ) J.

Now, apply the formula:
`\( p = (1.602 * 10⁻¹⁶)/(3.00 * 10⁸)` m/s (speed of light). The result is approximately ( 5.02 \times 10⁻²³ ) kg·m/s.

This calculation shows that the momentum of the 100 keV x-ray photon is ( 5.02 x 10⁻²³ ) kg·m/s.