Physics
Physics
5th Edition
ISBN: 9781260487008
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 27, Problem 27P
To determine

The velocity of the scattered electron.

Expert Solution & Answer
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Answer to Problem 27P

The velocity of the scattered electron is 4.45×106m/s at 62.6°south of east_.

Explanation of Solution

Given that the wavelength of the photon is 0.14800nm, it is travelling in the eastward direction, the wavelength of the scattered photon is 0.14900nm. It is obtained that the angle of scattering is 54.0°, and the south component of electron’s momentum is 3.60×1024kgm/s.

Write the expression for the south component of electron’s momentum.

  pe,south=mevs                                                                                                         (I)

Here, pe,south is the south component of electron’s momentum, me is the mass of electron, and vs is the south component of electron’s velocity.

Write the expression for the north component of the scattered photon’s momentum.

  pnorth=hλsinθ                                                                                                    (II)

Here, pnorth is the north component of scattered momentum, h is the Planck’s constant, λ is the wavelength of scattered photon, and θ is the scattering angle.

Since the south component of electron’s momentum is equal to the north component of the scattered photon’s momentum, the right hand sides of equations (I) and (II) can be equated.

  mevs=hλsinθ                                                                                                    (III)

Solve equation (III) for vs.

  vs=hmeλsinθ                                                                                                   (IV)

Write the expression for the east component of electron’s momentum.

  pe,east=meve                                                                                                        (V)

Here, pe,east is the east component of electron’s momentum, and ve is the east component of electron’s velocity.

Write the expression for the east component of electron’s momentum in terms of the momentum of the photon.

  pe,east=ppeast                                                                                                  (VI)

Here, p is the momentum of the incident photon, and peast is the east component of momentum of scattered photon.

Modify equation (VI) by replacing the momentum of photons in terms of their wavelength and using equation (V).

  meve=hλhλcosθ                                                                                            (VII)

Solve equation (VII) for ve.

  ve=hme(1λcosθλ)                                                                                         (VIII)

Write the expression for the expression for the magnitude of velocity of the scattered electron.

  v=vs2+ve2                                                                                                        (IX)

Write the expression for the angle that the scattered electrons velocity make with the east direction.

  ϕ=tan1(vsve)                                                                                                   (X)

Here, ϕ is the angle that the scattered electrons velocity make with the east direction.

Conclusion:

Substitute 6.626×1034Js for h, 9.109×1031kg for me, 0.14900nm for λ, and 54.0° for θ in equation (IV) to find vs.

  vs=6.626×1034Js(9.109×1031kg)(0.14900nm)sin54.0°=6.626×1034Js(9.109×1031kg)(0.14900nm×1m1×109nm)sin54.0°=3.95×106m/s

Substitute 6.626×1034Js for h, 9.109×1031kg for me, 0.14800nm for λ, 0.14900nm for λ, and 54.0° for θ in equation (VIII) to find ve.

  ve=6.626×1034Js9.109×1031kg(10.14800nmcos54.0°0.14900nm)=6.626×1034Js9.109×1031kg(10.14800nmcos54.0°0.14900nm)(1×109nm1m)=2.05×106m/s

Substitute 3.95×106m/s for vs, and 2.05×106m/s for ve in equation (IX) to find v.

  v=(3.95×106m/s)2+(2.05×106m/s)2=4.45×106m/s

Substitute 3.95×106m/s for vs, and 2.05×106m/s for ve in equation (X) to find ϕ.

  ϕ=tan1(3.95×106m/s2.05×106m/s)=62.6°

This indicates that the electron travels in a direction 62.6° south of east.

Therefore, the velocity of the scattered electron is 4.45×106m/s at 62.6°south of east_.

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Chapter 27 Solutions

Physics

Ch. 27.7 - Prob. 27.7PPCh. 27.7 - Prob. 27.8PPCh. 27.8 - Prob. 27.9PPCh. 27 - Prob. 1CQCh. 27 - Prob. 2CQCh. 27 - Prob. 3CQCh. 27 - Prob. 4CQCh. 27 - Prob. 5CQCh. 27 - Prob. 6CQCh. 27 - Prob. 7CQCh. 27 - Prob. 8CQCh. 27 - Prob. 9CQCh. 27 - Prob. 10CQCh. 27 - Prob. 11CQCh. 27 - Prob. 12CQCh. 27 - Prob. 13CQCh. 27 - Prob. 14CQCh. 27 - Prob. 15CQCh. 27 - Prob. 16CQCh. 27 - Prob. 17CQCh. 27 - Prob. 18CQCh. 27 - Prob. 19CQCh. 27 - Prob. 20CQCh. 27 - Prob. 21CQCh. 27 - Prob. 22CQCh. 27 - Prob. 23CQCh. 27 - Prob. 1MCQCh. 27 - Prob. 2MCQCh. 27 - Prob. 3MCQCh. 27 - Prob. 4MCQCh. 27 - Prob. 5MCQCh. 27 - Prob. 6MCQCh. 27 - Prob. 7MCQCh. 27 - Prob. 8MCQCh. 27 - Prob. 9MCQCh. 27 - Prob. 10MCQCh. 27 - Prob. 1PCh. 27 - Prob. 2PCh. 27 - Prob. 3PCh. 27 - Prob. 4PCh. 27 - Prob. 5PCh. 27 - Prob. 6PCh. 27 - Prob. 7PCh. 27 - Prob. 8PCh. 27 - Prob. 9PCh. 27 - Prob. 10PCh. 27 - Prob. 11PCh. 27 - Prob. 12PCh. 27 - Prob. 13PCh. 27 - Prob. 14PCh. 27 - Prob. 15PCh. 27 - Prob. 16PCh. 27 - Prob. 17PCh. 27 - Prob. 18PCh. 27 - Prob. 19PCh. 27 - Prob. 20PCh. 27 - Prob. 21PCh. 27 - Prob. 22PCh. 27 - Prob. 23PCh. 27 - Prob. 24PCh. 27 - Prob. 25PCh. 27 - Prob. 26PCh. 27 - Prob. 27PCh. 27 - Prob. 28PCh. 27 - Prob. 29PCh. 27 - Prob. 30PCh. 27 - Prob. 31PCh. 27 - Prob. 32PCh. 27 - Prob. 33PCh. 27 - Prob. 34PCh. 27 - Prob. 35PCh. 27 - Prob. 36PCh. 27 - Prob. 37PCh. 27 - Prob. 38PCh. 27 - Prob. 39PCh. 27 - Prob. 40PCh. 27 - Prob. 41PCh. 27 - Prob. 42PCh. 27 - Prob. 43PCh. 27 - Prob. 44PCh. 27 - Prob. 45PCh. 27 - Prob. 46PCh. 27 - Prob. 47PCh. 27 - Prob. 48PCh. 27 - Prob. 49PCh. 27 - Prob. 50PCh. 27 - Prob. 51PCh. 27 - Prob. 52PCh. 27 - Prob. 53PCh. 27 - Prob. 54PCh. 27 - Prob. 55PCh. 27 - Prob. 56PCh. 27 - Prob. 57PCh. 27 - Prob. 58PCh. 27 - Prob. 59PCh. 27 - Prob. 61PCh. 27 - Prob. 60PCh. 27 - Prob. 62PCh. 27 - Prob. 64PCh. 27 - Prob. 63PCh. 27 - Prob. 66PCh. 27 - Prob. 65PCh. 27 - Prob. 68PCh. 27 - Prob. 67PCh. 27 - Prob. 70PCh. 27 - Prob. 69PCh. 27 - Prob. 72PCh. 27 - Prob. 71PCh. 27 - Prob. 74PCh. 27 - Prob. 73PCh. 27 - Prob. 75PCh. 27 - Prob. 76PCh. 27 - Prob. 77PCh. 27 - Prob. 78PCh. 27 - Prob. 79PCh. 27 - Prob. 80PCh. 27 - Prob. 82PCh. 27 - Prob. 81PCh. 27 - Prob. 84PCh. 27 - Prob. 83PCh. 27 - Prob. 86PCh. 27 - Prob. 85PCh. 27 - Prob. 88PCh. 27 - Prob. 87PCh. 27 - Prob. 89PCh. 27 - Prob. 90PCh. 27 - Prob. 91PCh. 27 - Prob. 92PCh. 27 - Prob. 93PCh. 27 - Prob. 94PCh. 27 - Prob. 95PCh. 27 - Prob. 96P
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