modern physics - relativity

posted by .

A photon of energy E collides with a stationary particle of rest mass m0 and is absorbed by it .

(A) what is the velocity of resulting composite particle ?

(B) What is the mass of the resulting composite particle ?

use conservasion of energy / momentum please show working

  • modern physics - relativity -

    A) You can find the velocity by cmputing the total energy and momentum. From:

    E = gamma m c^2

    and

    P = gamma m v

    it follows that

    p/E = v/c^2

    The total energy is:

    E + m0 c^2

    The total momentum is the momentum of the photon, which is E/c. The total energy and momentum are conserved, so these are the energy and momentum of the particle after the photon has been absorbed. The velocity of that particle is thus:

    v = c^2 momentum/energy =

    c^2 E/c 1/(E + m0 c^2 ) =

    E c/(E + m0 c^2)


    The mass follows from the invariant:

    E^2 - p^2 c^2

    Fora system with eenrgy E and momentum p, this quantity has the same valyue in all frames. If you evaluate this in the rest frame then p = 0 and E = m c^2, so it is E^2 = m^2 c^4. The fact tha the quatity is invariant, means that it has this value in any frame. This means that given the enrgy and momentum of a system, you can compute the mass:

    m^2 = E^2/c^4 - p^2/c^2

    In this case, you find:

    m^2 = (E + m0 c^2)^2/c^4 - E^2/c^4 =

    2 m0 E/c^2 + m0^2

    So, the mass is:

    m = m0 sqrt[1 + 2 E/(m0 c^2)]

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus - limits

    In the theory of relativity, the mass of a particle with velocity v is m = m0 / sqrt(1-v^2 / c^2) where m0 is mass of the particle at rest and c is the speed of light. What happens as v approaches c^-?
  2. math

    In the theory of relativity, the mass of a particle with velocity v is m=mo/(square root ((1- v^ 2)/ c^2)) where mo is the mass of the particle at rest and ci s the speed of light. What happens as v goes to c?
  3. Calculus

    I don't understand this question. Q. In the theory of relativity, the mass of a particle with velocity "v" is m = mo/√(1-v2/c2) where mo is the mass of the particle at rest and "c" is the speed of light. What happends as v-->c-?
  4. Physics

    A particle with m = 3.3E-27 kg is moving with a velocity of 6.0E7m/s. It then collides with a stationary particle of mass 2m, the lighter particle then moves at a right angle to the original direction with a velocity of 2.0E7m/s. What …
  5. special relativity

    A photon of energy E collides with a stationary particle of rest mass m0 and is absorbed by it. what is the velocity of the resulting composite particle ?
  6. physics emergerncyy!

    A particle of mass m1 = 2.5 kg moving along the x axis collides with a particle of mass m2 = 4.7 kg initially at rest. The incoming particle is deflected in the direction 24 degrees above the x axis, whereas the target particle moves …
  7. Math

    A particle A of mass 2.11 kg collides with another particle B of mass 3.86 kg. Their initial velocities are u1 = 2.16i + 0.88j and u2 = 0.7i + 1.12j just before impact. After collision, they both merged and becomes a composite particle, …
  8. Physics

    The kinetic energy of a massive particle is equal to the energy of a photon.  The massive particle moves at 1.49 % the speed of light.     What is the ratio of the photon wavelength to the de Broglie wavelength of the particle?
  9. Physics

    A particle of mass m1 = 2.5 kg moving along the x axis collides with a particle of mass m2 = 4.9 kg initially at rest. The incoming particle is deflected in the direction 22 degrees above the x axis, whereas the target particle moves …
  10. Physics

    The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 6.9% of the speed of light. Find the ratio of the photon wavelength to the de Broglie wavelength of the particle. Take the speed to be non-relativistic.

More Similar Questions