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Chapter 26: Problem 51

An electron has a total energy of 6.5 MeV. What is its momentum (in MeV/c)?

Short Answer

Expert verified
Answer: The momentum of the electron is approximately 6.44 MeV/c.

Step by step solution

01

Write down given values and relativistic energy-momentum equation

Write the relativistic energy-momentum equation, the mass of an electron, and the given total energy: \(E^2 = (mc^2)^2 + (pc)^2\) \(E = 6.5 \,\text{MeV}\) \(m = 0.511 \,\text{MeV}/c^2\)
02

Rewrite equation in terms of momentum (p)

Solve the relativistic energy-momentum equation for momentum \(p\), by isolating it on one side of the equation: \((pc)^2 = E^2 - (mc^2)^2\)
03

Input the given values and calculate the momentum

Substitute the given total energy and electron mass into the equation: \((p \cdot c)^2 = (6.5 \,\text{MeV})^2 - (0.511 \,\text{MeV}/c^2 \cdot c^2)^2\) Now, calculate the value of the right side of the equation: \((p \cdot c)^2 = (6.5 \,\text{MeV})^2 - (0.511 \,\text{MeV})^2\)
04

Determine the momentum p

To find the momentum \(p\), take the square root of both sides of the equation: \(p \cdot c = \sqrt{(6.5 \,\text{MeV})^2 - (0.511 \,\text{MeV})^2}\) Calculate the value of the right side: \(p \cdot c ≈ 6.44 \,\text{MeV}\) So, the momentum of the electron is approximately 6.44 MeV/c.

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Most popular questions from this chapter

Suppose your handheld calculator will show six places beyond the decimal point. How fast (in meters per second) would an object have to be traveling so that the decimal places in the value of \(\gamma\) can actually be seen on your calculator display? That is, how fast should an object travel so that \(\gamma=1.000001 ?\) [Hint: Use the binomial approximation.]
A futuristic train moving in a straight line with a uniform speed of \(0.80 c\) passes a series of communications towers. The spacing between the towers, according to an observer on the ground, is \(3.0 \mathrm{km} .\) A passenger on the train uses an accurate stopwatch to see how often a tower passes him. (a) What is the time interval the passenger measures between the passing of one tower and the next? (b) What is the time interval an observer on the ground measures for the train to pass from one tower to the next?
Two spaceships are observed from Earth to be approaching each other along a straight line. Ship A moves at \(0.40 c\) relative to the Earth observer, and ship \(\mathrm{B}\) moves at \(0.50 c\) relative to the same observer. What speed does the captain of ship A report for the speed of ship B?
A spaceship travels at constant velocity from Earth to a point 710 ly away as measured in Earth's rest frame. The ship's speed relative to Earth is $0.9999 c .$ A passenger is 20 yr old when departing from Earth. (a) How old is the passenger when the ship reaches its destination, as measured by the ship's clock? (b) If the spaceship sends a radio signal back to Earth as soon as it reaches its destination, in what year, by Earth's calendar, does the signal reach Earth? The spaceship left Earth in the year 2000.
Rocket ship Able travels at \(0.400 c\) relative to an Earth observer. According to the same observer, rocket ship Able overtakes a slower moving rocket ship Baker that moves in the same direction. The captain of Baker sees Able pass her ship at \(0.114 c .\) Determine the speed of Baker relative to the Earth observer.
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