An x-ray photon collides head-on with an electron and is scattered directly back at 160◦ to

its original direction.

What is the shift in the wavelength of the incident x-ray?

do i need to figure out the "compton shift" in order to solve..can someone please show me how to do this problem? Please and thank you so much!

delta wavelength=.00243(1-cos theta)

Yes, it is a Compton shift problem. The "theta" that you use is 160 degrees, which is the angle that the X-ray photon is scattered. (The electron is scattered at a different angle).

Your 0.00243 constant is actually
h/(mc), where h is Planck's constant and m is the electron mass. You need to say what the units are.
h/mc = 2.43*10^-10 cm according to my textbook. That would be 2.43*10-2 Angstroms or 2.43*10^-3 nanometers (nm)

The equation you wrote down apparently uses nanometers.

The wavelength change is 1.94*2.43*10^-3 = 4.7*10^-3 nm, or 47 Angstroms

The scattered wavelength is longer by that amount.

My 'nanometers' number is correct, but would be 4.7*10^-2 Angstroms

X-ray wavelengths are typically 0.01 to 10 nm, which is 0.1 to 100 Angstroms

The Angstroms unit of wavelength seems to be less fashionable, although most "wavelength tables" published in the past used Angstroms

To solve this problem, you need to apply the Compton scattering formula to find the shift in the wavelength of the incident x-ray. The Compton scattering formula gives the change in wavelength (∆λ) of a photon as it scatters off an electron:

∆λ = λ' - λ = h / (m_e * c) * (1 - cos(θ))

Where:
- ∆λ is the change in wavelength (in meters).
- λ' is the scattered wavelength.
- λ is the incident wavelength.
- h is the Planck's constant (6.626 x 10^-34 J·s).
- m_e is the electron mass (9.109 x 10^-31 kg).
- c is the speed of light (3.00 x 10^8 m/s).
- θ is the scattering angle.

In this case, since the photon is scattered directly back at 160 degrees (180-160 = 20 degrees), we can use θ = 20 degrees.

Step-by-step solution:
1. Convert the angle from degrees to radians: θ_rad = θ_deg * π / 180 = 20 * π / 180 = 0.349066 radians.
2. Plug the values into the Compton scattering formula:

∆λ = h / (m_e * c) * (1 - cos(0.349066))

3. Calculate the shift in wavelength.

Now, let's calculate: