A 100 MeV photon collides with a resting prion. Calculate the maximum energy loss that the photon can suffer.

Baladdaa9 2022-07-17 Answered
A 100 MeV photon collides with a resting prion. Calculate the maximum energy loss that the photon can suffer.
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Answers (1)

autosmut6p
Answered 2022-07-18 Author has 8 answers
For the photon:
E 1 = h c λ 1 λ 1 = h c E 1
Substitute 100 × 10 6  eV for E 1 ,   3 × 10 8  m/s for c, and 6.63 × 10 34   J s for h
λ 1 = ( 6.63 × 10 34   J s ) ( 3 × 10 8  m/s ) ( 100 × 10 6  eV ) = ( 6.63 × 10 34   J s ) ( 3 × 10 8  m/s ) ( 100 × 10 6  eV ) × ( 1.6 × 10 19   J 1  eV ) = ( 6.63 × 10 34   J s ) ( 3 × 10 8  m/s ) ( 100 × 10 6 × 1.6 × 10 19 ) J λ 1 = 12.43125 × 10 15   m
By using the Compton's effect:
λ 2 λ 1 = h m p c ( 1 cos θ )
Here, the maximum possible change of energy takes place when the photon recoils in the opposite direction to that of the incident direction.
When cos θ = 1 therefore,
θ = cos 1 ( 1 ) θ = 180
Substitute 12.43125 × 10 15   m for λ 1 ,   180 for θ , 1.6 × 10 27   k g for m p , 3 × 10 8  m/s for c, and 6.63 × 10 34   J s for h into equation.
λ 2 12.4 × 10 15   m = 6.63 × 10 34   J s ( 1.6 × 10 27  kg ) ( 3 × 10 8  m/s ) ( 1 cos 180 ) λ 2 12.4 × 10 15   m = 2.76 × 10 15 λ 2 = 15.16 × 10 15   m
The lose of energy is,
E = E 2 E 1 = h c λ 2 h c λ 1
So:
E = 6.63 × 10 34 J s × 3 × 10 8  m/s 15.16 × 10 15   m 6.63 × 10 34 J s × 3 × 10 8  m/s 12.4 × 10 15   m = 1.312 × 10 11   J 1.604 × 10 11   J E = 2.916 × 10 11   J
Hence, the maximum energy loss that the photon can suffer is 2.916 × 10 11   J
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