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Chapter 5: Problem 59

What is the rest energy of an electron, given its mass is \(9.11 \times 10^{-31} \mathrm{kg} ?\) Give your answer in joules and \(\mathrm{MeV}\)

Short Answer

Expert verified
The rest energy of the electron is \(8.187 \times 10^{-14} \mathrm{J}\) or \(0.511 \mathrm{MeV}\).

Step by step solution

01

Write down the given values

We are given the mass of the electron: \(m = 9.11 \times 10^{-31} \mathrm{kg}\) and the speed of light in a vacuum: \(c = 2.998 \times 10^8 \mathrm{m/s}\).
02

Calculate the rest energy in joules

We will use Einstein's energy-mass relationship to calculate the rest energy: \(E = mc^2\) Plug in the given values: \(E = (9.11 \times 10^{-31} \mathrm{kg}) (2.998 \times 10^8 \mathrm{m/s})^2\) Calculate the energy: \(E = 8.187 \times 10^{-14} \mathrm{J}\)
03

Convert the rest energy from joules to MeV

To convert the energy from joules to MeV, we can use the conversion factor: \(1 \mathrm{MeV} = 1.602 \times 10^{-13} \mathrm{J}\) Divide the energy in joules by the conversion factor: \(E = \frac{8.187 \times 10^{-14} \mathrm{J}}{1.602 \times 10^{-13} \mathrm{J/MeV}}\) Calculate the energy: \(E = 0.511 \mathrm{MeV}\) So, the rest energy of the electron is \(8.187 \times 10^{-14} \mathrm{J}\) or \(0.511 \mathrm{MeV}\).

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Most popular questions from this chapter

(a) What is \(\gamma\) if \(v=0.100 c ?\) (b) If \(v=0.900 c ?\)

(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given \(0.750\space \mathrm{MeV}\) of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.

(a) Show that \((p c)^{2} /\left(m c^{2}\right)^{2}=\gamma^{2}-1 .\) This means that at large velocities \(p c>>m c^{2} .\) (b) Is \(E \approx p c\) when \(\gamma=30.0, \quad\) as for the astronaut discussed in the twin paradox?

Show that the relativistic form of Newton's second law is (a) \(F=m \frac{d u}{d t} \frac{1}{\left(1-u^{2} / c^{2}\right)^{3 / 2}} ;\) (b) Find the force needed to accelerate a mass of \(1 \mathrm{kg}\) by \(1 \mathrm{m} / \mathrm{s}^{2}\) when it is traveling at a velocity of \(c / 2\).

(a) A nuclear power plant converts energy from nuclear fission into electricity with an efficiency of \(35.0 \%\) How much mass is destroyed in one year to produce a continuous 1000 MW of electric power? (b) Do you think it would be possible to observe this mass loss if the total mass of the fuel is \(10^{4} \mathrm{kg}\) ?
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