A X-ray photon is scattered at an angle of 180 from an electron that is initially at rest. after scattering, the electron has a speed of 4.3x10^-6 m/s. find the wavelength of the incident x-ray photon.
To find the wavelength of the incident X-ray photon, we can use the principle of conservation of energy and momentum.
First, let's analyze the situation:
1. The X-ray photon is scattered at an angle of 180°, which means it is scattered directly backward.
2. The electron is initially at rest before the scattering.
3. After scattering, the electron has a speed of 4.3x10^-6 m/s.
Now, let's calculate the wavelength:
1. Conservation of momentum tells us that the initial momentum of the system (which is zero since the electron is initially at rest) must be equal to the final momentum of the system.
2. The momentum of a photon can be expressed as p = h/λ, where h is the Planck's constant and λ is the wavelength of the photon.
3. Since the electron is initially at rest, the final momentum of the system is equal to the momentum of the electron after scattering.
4. Therefore, h/λ_initial = m * v_final, where m is the mass of the electron and v_final is the final speed of the electron after scattering.
5. Rearranging the equation, we have λ_initial = h / (m * v_final).
6. Now, plug in the known values:
- Planck's constant (h) = 6.62607015 × 10^-34 J.s
- Mass of an electron (m) = 9.10938356 × 10^-31 kg
- Final speed of the electron (v_final) = 4.3x10^-6 m/s
λ_initial = (6.62607015 × 10^-34 J.s) / ((9.10938356 × 10^-31 kg) * (4.3x10^-6 m/s))
7. Calculate the result to find the wavelength of the incident X-ray photon.