Worksheet: Mass-Energy Equivalence

In this worksheet, we will practice calculating the rest mass-energy of massive objects and how much energy is required to produce particles with given masses.

Q1:

The amount of energy needed to create a tauon–antitauon pair is 3,560 MeV. An electron has a rest mass of 5 1 1 / 𝑐 k e V . How many times more massive is a tauon than an electron? Give your answer to 3 significant figures.

Q2:

If a metal sphere has a rest mass energy of 4 . 5 × 1 0 J, what is its rest mass? Give your answer to 2 significant figures.

Q3:

A proton has a rest mass of 1 . 6 7 × 1 0 kg. What is the rest mass energy of a proton? Give your answer to 3 significant figures.

  • A 9 . 8 1 × 1 0 J
  • B 1 . 5 0 × 1 0 J
  • C 5 . 5 7 × 1 0 J
  • D 3 . 0 0 × 1 0 J
  • E 1 . 5 0 × 1 0 J

Q4:

A neutron has a rest mass of 940 MeV/ 𝑐 . What is the rest mass energy of a neutron in mega-electron volts?

Q5:

A photon with an energy of 1 . 6 4 × 1 0 J has just enough energy to create an electron–positron pair. What is the rest mass of an electron? Give your answer in kilograms to 3 significant figures.

  • A 7 . 9 8 × 1 0 kg
  • B 1 . 8 2 × 1 0 kg
  • C 9 . 1 1 × 1 0 kg
  • D 1 . 8 2 × 1 0 kg
  • E 5 . 4 7 × 1 0 kg

Q6:

What is the rest mass energy of a 2 kg metal cube?

  • A 1 . 8 × 1 0 J
  • B 4 . 5 × 1 0 J
  • C 9 . 0 × 1 0 J
  • D 3 . 0 × 1 0 J
  • E 6 . 0 × 1 0 J

Q7:

A photon with an energy of 1,080 keV decays into an electron–positron pair. The rest mass of both the electron and the positron is 511 keV/c2. Any energy that is not used to produce the two massive particles goes into the relativistic kinetic energy of the particles. What is the relativistic kinetic energy of the positron?

Q8:

A muon has a mass of 106 MeV/c2. What energy would a single photon need to have to be able to produce a muon–antimuon pair? Give your answer in mega-electron volts (MeV).

Q9:

One metric ton of TNT releases 4.18 GJ of energy when it explodes. When hydrogen comes into contact with antihydrogen, the two annihilate. How many grams of hydrogen and antihydrogen are needed to release the same amount of energy as one metric ton of TNT?

  • A 4 . 1 8 × 1 0 g
  • B 4 . 6 4 × 1 0 g
  • C 4 . 6 4 × 1 0 g
  • D 4 . 1 8 × 1 0 g
  • E 4 . 6 4 × 1 0 g

Q10:

A spaceship has a rest mass of 10,000 metric tons. What is its rest mass energy? Answer to one significant figure.

  • A 1 × 1 0 J
  • B 9 × 1 0 J
  • C 9 × 1 0 J
  • D 3 × 1 0 J
  • E 3 × 1 0 J

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