quantum physics

After a .800-nm x-ray photon scatters from a free electron, the electron recoils with a speed equal to 1.20 x 10^6 m/s. (a) What was the Compton Shift in the photon's wavelength? (b) Through what angle was the photon scattered?

I got an answer for (a), but when i use it to find (b) the solution does not exist. I clearly did something wrong, and I can't figure it out.

  1. 👍 0
  2. 👎 0
  3. 👁 429
  1. a) follows from conservation of energy:

    Photon energy + m = photon energy after collision plus gamma m

    (in c = 1 units)

    In b) you have to take into account that both the photon after the collision and the electron after the collison are not moving in the same direction the incident photon was moving.

    The simplest way to solve this problem is by writing conservation of energy and momentum as a single four-momentum equation:

    pf + pe = qf + qe (1)

    where

    pf = four-mometum of photon before collision

    pe = four-momentum of electron before collision

    qf = four-mometum of photon after collision

    qe = four-momentum of electron after collision

    We are not interested in qe, so we want to eliminate it from the equation. What we do is we write (1) as:

    qe = pf + pe - qf

    We then square both sides:

    qe^2 = (pf + pe - qf)^2 =

    pf^2 + pe^2 + qf^2 + 2 pf dot pe +

    - 2 pf dot qf -2 pe dot qf

    Next substitute the energy momentum relation p^2 = m^2, so we have:

    qe^2 = m^2

    pe^2 = m^2

    pf^2 = 0

    qf^2 = 0

    and the equation simplifies to:

    2 pf dot pe - 2 pf dot qf -2 pe dot qf = 0

    Pf dot qf contains the angle you want to know. Pe = (m,0,0) because the electron before the collision was at rest, so the Lorentz inner product of the two other terms are just the electron mass times the photon energies.

    1. 👍 0
    2. 👎 0
  2. How much force will be needed to give a 10kg body resting on the ground an upward acceleration of 5m/s if acceleration due to gravity at the place is 10.02m/s?

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    The energies, E, for the first few states of an unknown element are shown here in arbitrary units: n= 1, E=-21 n=2, E=-9 n=3, E=-4 n=4, E=-3 ...,... infinity, 0 A gaseous sample of this element is bombarded by photons of various

  2. The Binding Energy of Electrons?

    An X-ray photon of wavelength 0.954 nm strikes a surface. The emitted electron has a kinetic energy of 935 eV. What is the binding energy of the electron in kJ/mol? [KE =1/2 mv^2; 1 electron volt (eV) = 1.602 x 10^- 19 J]

  3. Nuclear Chemistry

    The half- life of a positron is very short. it reacts with an electron, and the masses of both are converted to two gamma-ray photons: (0e+1)+ (0e-1)---> 2γ (the 0 in front of e is the mass # and behind it is the atomic #) (γ

  4. physics

    An electron is accelerated from rest through a potential difference that has a magnitude of 2.90 × 107 V. The mass of the electron is 9.11 × 10-31 kg, and the negative charge of the electron has a magnitude of 1.60 × 10-19 C.

  1. Physics

    Zinc has a work function of 4.30 ev . A 4.50eV photon strikes the surface and an electron is emitted. What is the maximum possible speed of the electron?

  2. Chemistry

    The energies, E, for the first few states of an unknown element are shown here in arbitrary units. n 1 E -11 n 2 E -5 n 3 E -2 n 4 E -1 n ... E ... n infinite E 0 A gaseous sample of this element is bombarded by photons of various

  3. Physics

    A photon having wavelength λ scatters off a free electron at A (see figure below), producing a second photon having wavelength λ'. This photon then scatters off another free electron at B, producing a third photon having

  4. Chem

    Hello What is the wavelength (in nm) of the line in the spectrum of the hydrogen atom that arises from the transition of the electron from the orbital with n =5 to the orbital with n = 2? Note, the line corresponds to the energy

  1. PHYSICS 2

    An electron in an x-ray machine is accelerated through a potential difference of 1x10^4 V before it hits the target. What is the kinetic energy of the electron in electron volts?

  2. Chemistry (Electrons in Atoms)

    True or False. 1)Electrons give off light as they drop to lower energy levels. 2)Electrons travel around the nucleus as waves. 3)A photon of low frequency light has more energy than a photon of high frequency light. 4)Orbitals

  3. Physics

    Find energy of an X-ray photon which can impart maximum energy of 50 keV to electron?

  4. physics

    a) If a photon and an electron each have the same energy of 20.0 eV, find the wavelength of each. b) If a photon and an electron each have the same wavelength of 250 nm, find the energy of each. c) You want to study an organic

You can view more similar questions or ask a new question.