Question

Фотон с энергией 0,3 МэВ рассеялся под углом 30 градусов на свободном электроне. Определить энергию рассеянного фотона и кинетическую энергию электрона отдачи.

Answer 1

L'-L=h*(1-cosa)/m0*c
h*c/E' -h*c/E=h*(1-cosa)/m0*c   1/E' -1/E=(1-cosa)/m0c^2   m0*c^2=E0=0,51 МэВ
E'=E/((E*(1-cosa)/E0)+1=0,3/(0,3*(1-0,87/0,51)+1=0,28 МэВ
Ek=E-E'=0,3-0,28=0,02 МэВ

Answer 2

Calculation of the Scattered Photon's Energy and the Recoil Electron's Kinetic Energy

To determine the energy of the scattered photon and the kinetic energy of the recoil electron, we can use the principles of conservation of energy and momentum.

Let's denote the initial energy and momentum of the photon as E1 and p1, respectively. Similarly, the final energy and momentum of the scattered photon will be denoted as E2 and p2, and the kinetic energy and momentum of the recoil electron as KE and p3, respectively.

According to the conservation of energy, the initial energy of the photon (E1) will be equal to the sum of the final energy of the scattered photon (E2) and the kinetic energy of the recoil electron (KE):

E1 = E2 + KE (Equation 1)

Additionally, according to the conservation of momentum, the initial momentum of the photon (p1) will be equal to the sum of the final momentum of the scattered photon (p2) and the momentum of the recoil electron (p3):

p1 = p2 + p3 (Equation 2)

Given that the energy of the photon is 0.3 MeV and it is scattered at an angle of 30 degrees, we can proceed with the calculations.

To determine the energy of the scattered photon (E2), we can use the equation for the conservation of energy (Equation 1). However, we need to know the kinetic energy of the recoil electron (KE) to solve for E2.

To find the kinetic energy of the recoil electron (KE), we can use the equation for the conservation of momentum (Equation 2). However, we need to know the momentum of the scattered photon (p2) to solve for KE.

Let's calculate the momentum of the scattered photon (p2) using the given information.

Calculation of the Momentum of the Scattered Photon (p2)

The momentum of a photon can be calculated using the equation:

p = E/c (Equation 3)

Where p is the momentum, E is the energy, and c is the speed of light.

Given that the energy of the photon is 0.3 MeV, we can convert it to joules by multiplying it by the conversion factor 1.6 x 10^-13 J/MeV.

E1 = 0.3 MeV * 1.6 x 10^-13 J/MeV = 4.8 x 10^-14 J (Equation 4)

Using Equation 3, we can calculate the momentum of the scattered photon (p2):

p2 = E2/c (Equation 5)

Now, let's calculate the momentum of the scattered photon (p2).

p2 = E2/c = 4.8 x 10^-14 J / (2.9979 x 10^8 m/s) = 1.601 x 10^-22 kg·m/s (Equation 6)

Calculation of the Kinetic Energy of the Recoil Electron (KE)

Using Equation 2, we can calculate the kinetic energy of the recoil electron (KE):

p1 = p2 + p3 (Equation 7)

Since the initial momentum of the photon (p1) is equal to the momentum of the scattered photon (p2), we can rewrite Equation 7 as:

p2 = p2 + p3 (Equation 8)

Rearranging Equation 8, we can solve for the momentum of the recoil electron (p3):

p3 = p1 - p2 (Equation 9)

Substituting the values of p1 and p2, we can calculate p3:

p3 = p1 - p2 = p2 - p2 = 0 kg·m/s (Equation 10)

Since the momentum of the recoil electron (p3) is zero, we can conclude that the recoil electron is at rest after the scattering event.

Now, let's substitute the value of p3 into Equation 1 to solve for the energy of the scattered photon (E2):

E1 = E2 + KE (Equation 11)

Since the recoil electron is at rest (KE = 0), Equation 11 simplifies to:

E1 = E2 (Equation 12)

Substituting the value of E1 and solving for E2, we can determine the energy of the scattered photon (E2):

E2 = E1 = 0.3 MeV (Equation 13)

Therefore, the energy of the scattered photon is 0.3 MeV.

To summarize: - The energy of the scattered photon is 0.3 MeV. - The kinetic energy of the recoil electron is 0 J (at rest).

Please note that the calculations assume ideal conditions and neglect any other interactions or effects that may occur during the scattering process.

Let me know if there's anything else I can help you with!