calculate the maximum increase in photon wavelength that can occur during Compton Scattering. (answer in pm).
new lambda - old lambda = electron lambda (1-cos theta)
1-cos theta is max when theta = 180 degrees (cos theta = -1) and (1 -cos theta ) is two
electron wavelength is h/( me c)
= 2.43*10^-12 meters
so
4.86 * 10^-12 meters
To calculate the maximum increase in photon wavelength during Compton scattering, we can use the formula known as the Compton wavelength shift equation:
Δλ = (h / m_e * c) * (1 - cosθ)
Where:
Δλ is the change in wavelength
h is the Planck's constant (6.626 × 10^-34 J · s)
m_e is the rest mass of the electron (9.10938356 × 10^-31 kg)
c is the speed of light in a vacuum (299,792,458 m/s)
cosθ is the cosine of the angle between the incident photon and the scattered photon
In Compton scattering, the angle between the incident and scattered photons can vary from 0° to 180°. For the maximum increase in wavelength, we need to consider the case where the angle is 180°, which gives us the maximum energy transfer to the electron.
Plugging in the values into the formula, we get:
Δλ = (6.626 × 10^-34 J · s / (9.10938356 × 10^-31 kg) * (299,792,458 m/s)) * (1 - cos(180°))
Let's calculate this:
cos(180°) = -1, so our equation becomes:
Δλ = (6.626 × 10^-34 J · s / (9.10938356 × 10^-31 kg) * (299,792,458 m/s)) * (1 - (-1))
Simplifying further:
Δλ = (6.626 × 10^-34 J · s / (9.10938356 × 10^-31 kg) * (299,792,458 m/s)) * (2)
Now let's calculate the result:
Δλ = (6.626 × 10^-34 J · s / (9.10938356 × 10^-31 kg) * (299,792,458 m/s)) * (2) = 1.226 × 10^-12 meters
Therefore, the maximum increase in photon wavelength (Δλ) that can occur during Compton scattering is 1.226 picometers (pm).