After undergoing through 90 degree compton scattering, the fraction of energy lost by photon is
A) 10 %
B) 50 %
C) 20 %
D) Zero
E) None
50%
How it's 50
To find the fraction of energy lost by a photon after undergoing 90-degree Compton scattering, we need to understand the concept of Compton scattering and how it affects the energy of a photon.
Compton scattering is an interaction between a photon and a charged particle, typically an electron. During this interaction, the photon transfers part of its energy and momentum to the electron, resulting in a change in the photon's wavelength and direction.
The energy lost by the photon can be calculated using the Compton wavelength shift formula:
Δλ = λ' - λ = (h / (mec)) * (1 - cosθ)
Where:
Δλ is the change in wavelength,
λ' is the final wavelength,
λ is the initial wavelength,
h is the Planck's constant (6.626 x 10^-34 J*s),
me is the rest mass of an electron (9.109 x 10^-31 kg),
c is the speed of light (3 x 10^8 m/s),
θ is the scattering angle.
In the case of 90-degree scattering (θ = 90 degrees), the formula simplifies to:
Δλ = (2h / mec)
The change in wavelength corresponds to the change in the photon's energy, given by the equation:
ΔE = (hc / Δλ)
Now, let's calculate the fraction of energy lost by the photon:
Fraction of energy lost = (ΔE / E_initial) * 100
Since we know the initial angle (90 degrees), we can directly calculate the fraction of energy lost.
Calculating:
Δλ = (2 * 6.626 x 10^-34 J*s) / (9.109 x 10^-31 kg * (3 x 10^8 m/s))
ΔE = (6.626 x 10^-34 J*s * (3 x 10^8 m/s)) / [(2 * 6.626 x 10^-34 J*s) / (9.109 x 10^-31 kg * (3 x 10^8 m/s))]
Fraction of energy lost = (ΔE / E_initial) * 100
Now, by substituting the values and performing the calculations, we can determine the correct answer from the options provided.