Respuesta :
the magnitude of the linear momentum of the electron just after it collides with the photon is (7.558 × 10⁻²⁶) kgm/s.
Let the photon's wavelength before it collides. = λ
After a collision, the photon's wavelength equal = λ'
before a collision, the photon's frequency = f
After-collision photon frequency = f'
Pp = (h/) is the momentum of the photon prior to collision.
Prior to collision, the photon's momentum is given by Pp' = (h/'), where h is Planck's constant.
Let P represent the electron's post-collision momentum.
According to Compton's theory, the elastic collision between a photon and an electron abides by the principles of momentum and energy conservation.
The conservation of momentum
Momentum before collision = momentum after collision
Before momentum collision = Pp.
After-collision momentum = (Pp' + P)
Pₚ = (Pₚ' + P)
P = (Pp - Pp') = (h/) - (h/') = h[(1/) - (1/')]
With the exception of the photon's after-collision wavelength, all of the variables needed to determine the electron's momentum are known.
We utilize the Compton's wavelength formula to determine this.
Compton established from the principle of conservation of mass and momentum that the wavelength of the electron following a collision i λ's given by
λ' - λ = (h/m₀c) (1 - cos θ)
where; h = Planck's constant = 6.63 × 10⁻³⁴ J.s
m₀ = mass of the electron = 9.11 × 10⁻³¹ kg
c = speed of light = 3.0 × 10⁸ m/s
θ = angle of scattering of the photons after collision = 60°; cos 60° = 0.5
λ = 0.102 nm = 1.02 × 10⁻¹⁰ m
λ' - λ = [(6.63 × 10⁻³⁴/(9.11 × 10⁻³¹ × 3.0 × 10⁸)] × 0.5
λ' - λ = 1.213 × 10⁻¹² m
λ' = λ + (1.213 × 10⁻¹²) = (1.02 × 10⁻¹⁰) + (1.213 × 10⁻¹²) = (1.032 × 10⁻¹²) m
P = (Pₚ - Pₚ') = (h/λ) - (h/λ') = h[(1/λ) - (1/λ')]
P = h[(1/λ) - (1/λ')] = (6.63 × 10⁻³⁴) [(1/(1.02 × 10⁻¹⁰)) - (1/(1.032 × 10⁻¹²))] = (6.63 × 10⁻³⁴) (113999088) = (7.558 × 10⁻²⁶) kgm/s
Learn more about the Linear momentum with the help of the given link:
https://brainly.com/question/4126751
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