Chapter 44: Q54P (page 1368)

An electron and a positron, each with a kinetic energy of $2.500 MeV$ , annihilate, creating two photons that travel away in opposite directions. What is the frequency of each photon?

Short Answer

Expert verified

$7.3 \times 10^{20} Hz$

Step by step solution

Given data

Kinetic energy of each particle is

$K = 2.5 MeV$

Total relativistic energy and energy of a photon

The total energy of a particle carrying kinetic energy K and rest energy $E_{0}$ is

$E = K + E_{0} \cdot \cdot \cdot \cdot \cdot \cdot (1)$

The energy of a photon of frequency $ν$ is

$E = hν \cdot \cdot \cdot \cdot \cdot \cdot (2)$

Here h is the Planck's constant having value

$h = 6.6 \times 10^{- 34} J \cdot s$

Determining the frequency of the emitted photons

The rest energy of electron and positron is

$E_{0} = 0.51 MeV$

From equation (1) the total energy of the electron-positron pair is

$E = 2 \times (0.51 MeV + 2.5 MeV) = 2 \times 3.01 MeV$

Thus $3.0 MeV$ energy is carried away by each photon. This energy in Joule is

$E = 3.01 \times (1 MeV \times \frac{1.6 \times 10^{- 13} J}{1 MeV}) = 4.82 \times 10^{- 13} J$

From equation (2) the frequency of each photon is

$ν = \frac{E}{h} = \frac{4.82 \times 10^{- 13} J}{6.6 \times 10^{- 34} J \cdot s} = 7.3 \times 10^{20} s^{- 1} = 7.3 \times 10^{20} Hz$

Hence the frequency is

$7.3 \times 10^{20} Hz$

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An electron and a positron, each with a kinetic energy of $2.500 MeV$ , annihilate, creating two photons that travel away in opposite directions. What is the frequency of each photon?

Short Answer

Step by step solution

Given data

Total relativistic energy and energy of a photon

Determining the frequency of the emitted photons

One App. One Place for Learning.

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An electron and a positron, each with a kinetic energy of 2.500MeV, annihilate, creating two photons that travel away in opposite directions. What is the frequency of each photon?

Short Answer

Step by step solution

Given data

Total relativistic energy and energy of a photon

Determining the frequency of the emitted photons

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Kinematics Physics

Nuclear Physics

Energy Physics

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Study anywhere. Anytime. Across all devices.

An electron and a positron, each with a kinetic energy of $2.500 MeV$ , annihilate, creating two photons that travel away in opposite directions. What is the frequency of each photon?