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egoroff_w [7]
3 years ago
9

A photon of wavelength 15 x 10^-12 m hits an electron at rest, causing the electron to move. The photon bounces off the electron

at some angle θ relative to its original direction. If its new wavelength is 16 x 10^-12 m, what is θ? (a) 24° (b) 36° (c) 54° (d) 66°
Physics
1 answer:
BabaBlast [244]3 years ago
7 0

Answer:

c) 54°

Explanation:

let h be the planck constant, m be the mass of an electron and c be the speed of light. let λn be the new wavelength and λ be the initial wavelength. [h/(m×c)] = 2.43×10^-12 m.

then, according to compton effect:

          Δλ = [h/(m×c)]×(1 - cos(θ))

     λn - λ = [h/(m×c)]×(1 - cos(θ))

1 - cos(θ) = (λn - λ)/[h/(m×c)]

  cos(θ)  = 1 - (λn - λ)/[h/(m×c)]

   cos(θ) =  1 - (16×10^-12 - 15×10^-12)/[2.43×10^-12]

   cos(θ) = 0.5884773663

           θ = 53.95°

              ≈ 54°

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With the use of electric force formula, the direction and magnitude of the net force exerted on the point charge q3 are 9.9 x 10^{11} N and 66 degrees

ELECTRIC FORCE (F)

F = \frac{KQq}{d^{2} }

Where K = 9 x 10^{9} Nm^{2}/C^{2}

The distance between q_{1} and q_{3} can be calculated by using Pythagoras theorem.

d = \sqrt{33^{2} + 33^{2}  }

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Summation of forces on X component will be

F_{x} = F_{2} - F_{1} Cos 45

F_{x} = 4.96 x 10^{11} - 1.24 x 10^{11} Sin 45

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Net Force = \sqrt{F_{x} ^{2} + F_{y} ^{2}  } }

Net force = \sqrt{(4.08*10^{11}) ^{2} + (9.04*10^{11}) ^{2}  }

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The direction will be

Tan ∅ = F_{y}/F_{x}

Tan ∅ = 9.04 x 10^{11} / 4.08 x 10^{11}

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∅ = Tan^{-1}(2.216)

∅ = 65.7 degrees

Therefore, the direction and magnitude of the net force exerted on the point charge q3 are 9.9 x 10^{11} N and 66 degrees approximately.

Learn more about electric Force here: brainly.com/question/4053816

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