Question

An electron and a positron are moving toward each other with equal speeds of 3 x...

An electron and a positron are moving toward each other with equal speeds of 3 x 106 m/s. The two particles annihilate each other and produce two photons of equal energy. (a) Do you need to use relativity for this problem? Support your answer numerically, and comment intelligently. (b) What were the deBroglie wavelengths of the electron and positron? (c) Find the energy of each photon. (d) Find the momentum of each photon. (e) Find the wavelength of each photon.

Science   Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

a )

yes need to have relativity

given

speed is v = 3 X 106 m/s

v = 0.01 c ( since c = 3 X 108 m/s )

b )

deBroglie wavelength of electron is ele = h / m v

= 6.67 X 10-34 / 9.1 X 10-31 X 3 X 106

= 2.44 X 10-10 m

positron is also have same mass

deBroglie wavelength of electron is positron = h / m v

= 6.67 X 10-34 / 9.1 X 10-31 X 3 X 106

= 2.44 X 10-10 m

c )

KE = mc2 ( 1 /(1-v2/c2)1/2 - 1 )

= mc2 ( 1 /(1-0.012c2/c2)1/2 - 1 )

= mc2 ( 1 /(1-0.012c2/c2)1/2 - 1 )

KE = 5 X 10-5 X m c2

= 5 X 10-5 X 9.1 X 10-31 X 9 X 1016

KE = 4.095 X 10-18 J

E = moc2 + KE

= 9.1 X 10-31 X 3 X 108 + 4.095 X 10-18

= 4.095 X 10-18 J

d )

momentum

P = m v

= 9.1 X 10-31 X 3 X 106

= 2.73 X 10-24 kg.m/s

both are same for electron and positron .

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In a head-on collision of an electron of kinetic energy of 2.044 MeV with a positron...
In a head-on collision of an electron of kinetic energy of 2.044 MeV with a positron at rest, the two particles are replaced by two photons of equal energy. If each photon is traveling at an angles θ with respect to the electron’s direction of motion, What is the energy E, momentum p (you can leave the answer in terms of c) and angle of θ of each photon? (For electron and positron mc2 = 0.511 MeV)
An electron and an antielectron (positron) each have a rest energy of 0.511 MeV , or...
An electron and an antielectron (positron) each have a rest energy of 0.511 MeV , or approximately 8.2×10-14 J . When an electron and a positron are both stationary and located next to each other during an annihilation process, their mass energy converts to electromagnetic energy released as photons, electromagnetic particles that have momentum but no mass and that travel at the speed of light. What is the minimum number of photons that could be released, and how much energy...
An electron and a positron, each with a kinetic energy of 2.50 MeV, annihilate, creating two...
An electron and a positron, each with a kinetic energy of 2.50 MeV, annihilate, creating two photons that travel away in opposite directions.What is the frequency of each photon?
In Quantum Mechanics there's an interesting phenomenon where an electron and a positron collide. Since these...
In Quantum Mechanics there's an interesting phenomenon where an electron and a positron collide. Since these are antiparticles of each other, when they collide they annihilate and produce two equal energy photons. Why must this interaction produce two photons as opposed to one? Use some math in your logic.
In the medical diagnostic technique known as positron emission tomography (PET), a positron and an electron...
In the medical diagnostic technique known as positron emission tomography (PET), a positron and an electron annihilate each other and two γ–ray photons are emitted. What is the angle between the momentum vectors of the two photons? a. Zero degrees b. 45° c. Any angle is possible d. 90° e. 180°
Two particles are moving toward each other along the x axis with equal speeds. Specifically, particle...
Two particles are moving toward each other along the x axis with equal speeds. Specifically, particle 1 of mass 7 kg moves to the right at 3.87 m/s and particle 2 of mass 15 kg moves to the left at the same speed. The particles collide elastically. After the collision, the first particle moves at 90◦ to its original direction while the second particle is deflected through a smaller angle θ2 < 90◦. A) Find the final speed of particle...
Two particles with masses 4m and 3m are moving toward each other along the x axis...
Two particles with masses 4m and 3m are moving toward each other along the x axis with the same initial speeds vi. The particle with mass 4m is traveling to the left, and particle 3m is traveling to the right. They undergo a head-on elastic collision and each rebounds along the same line as it approached. Find the final speeds of the particles. particle 4m                                    
Two particles with masses 2m and 9m are moving toward each other along the x axis...
Two particles with masses 2m and 9m are moving toward each other along the x axis with the same initial speeds vi. Particle 2m is traveling to the left, while particle 9m is traveling to the right. They undergo an elastic glancing collision such that particle 2m is moving downward after the collision at right angles from its initial direction. (a) Find the final speeds of the two particles. particle 2m: ____ ✕ vi particle 9m: ____ ✕ vi (b)...
Two particles with masses m and 4m are moving toward each other along the x axis...
Two particles with masses m and 4m are moving toward each other along the x axis with the same initial speeds vi. Particle m is traveling to the left, while particle 4m is traveling to the right. They undergo an elastic, glancing collision such that particle m is moving in the negative y direction after the collision at a right angle from its initial direction. (a) Find the final speeds of the two particles in terms of vi. particle m__________...
Two protons are initially moving towards each other with equal speeds in the laboratory. They continue...
Two protons are initially moving towards each other with equal speeds in the laboratory. They continue to exist after experiencing a head-on collision that also produces a neutral pion of rest energy 135 MeV. If the protons and the pion are all at rest after the collision, find a) the initial kinetic energy of the protons, and b) the initial speed of the protons.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT