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E = mc² worksheet

Grades 8–9 · CCSS 8.EE.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Convert: Energy → mass
- Energy (E): 2 Mt TNT
- Show mass in: Kilograms (kg)
Find: Equivalent mass
Answer
2.
Problem 2.
- Convert: Energy → mass
- Energy (E): 2 Mt TNT
- Show mass in: Pounds (lb)
Find: Equivalent mass
Answer
3.
Problem 3.
- Convert: Mass → energy
- Mass (m): 1 g
- Show energy in: Kilowatt-hours (kWh)
Find: Equivalent energy
Answer
4.
Problem 4.
- Convert: Mass → energy
- Mass (m): 1 g
- Show energy in: Megaelectronvolts (MeV)
Find: Equivalent energy
Answer
5.
Problem 5.
- Convert: Energy → mass
- Energy (E): 1 Mt TNT
- Show mass in: Ounces (oz)
Find: Equivalent mass
Answer
6.
Problem 6.
- Convert: Energy → mass
- Energy (E): 2 Mt TNT
- Show mass in: Grams (g)
Find: Equivalent mass
Answer
7.
Problem 7.
- Convert: Energy → mass
- Energy (E): 2 Mt TNT
- Show mass in: Ounces (oz)
Find: Equivalent mass
Answer
8.
Problem 8.
- Convert: Mass → energy
- Mass (m): 2 g
- Show energy in: Electronvolts (eV)
Find: Equivalent energy
Answer
9.
Problem 9.
- Convert: Energy → mass
- Energy (E): 1 Mt TNT
- Show mass in: Daltons (atomic mass units) (Da)
Find: Equivalent mass
Answer
10.
Problem 10.
- Convert: Energy → mass
- Energy (E): 1 Mt TNT
- Show mass in: Metric tonnes (t)
Find: Equivalent mass
Answer

Answer key: E = mc² worksheet

1. Equivalent mass: 0.09 kg
1. Change energy to J, the standard unit the formula uses (1 Mt TNT = 4.184e+15 J)
  $2 Mt TNT \times 4.184e+15$ $= 8.368e+15 J$
2. To find the mass, divide the energy by the speed of light squared (c = 299,792,458 m/s)
  $\frac{8.368e+15}{{299,792,458}^{2}}$ $= 0.093106556691 kg$
2. Equivalent mass: 0.21 lb
1. Change energy to J, the standard unit the formula uses (1 Mt TNT = 4.184e+15 J)
  $2 Mt TNT \times 4.184e+15$ $= 8.368e+15 J$
2. To find the mass, divide the energy by the speed of light squared (c = 299,792,458 m/s)
  $\frac{8.368e+15}{{299,792,458}^{2}}$ $= 0.093106556691 kg$
3. Change the answer to lb, the unit you picked: divide by 0.45359237
  $\frac{0.093106556691}{0.45359237}$ $= 0.205264821122 lb$
3. Equivalent energy: 24,965,421.63 kWh
1. Change mass to kg, the standard unit the formula uses (1 g = 0.001 kg)
  $1 g \times 0.001$ $= 0.001 kg$
2. Square the speed of light (c), multiplying 299,792,458 m/s by itself
  ${299,792,458}^{2}$ $= 8.987552e+16 m²/s²$
3. Multiply the mass in kilograms by c² to get the energy in joules
  $0.001 \times 8.987552e+16$ $= 89,875,517,873,681.77 J$
4. Change the answer to kWh, the unit you picked: divide by 3,600,000
  $\frac{89,875,517,873,681.77}{3,600,000}$ $= 24,965,421.631578267 kWh$
4. Equivalent energy: 5.61e+26 MeV
1. Change mass to kg, the standard unit the formula uses (1 g = 0.001 kg)
  $1 g \times 0.001$ $= 0.001 kg$
2. Square the speed of light (c), multiplying 299,792,458 m/s by itself
  ${299,792,458}^{2}$ $= 8.987552e+16 m²/s²$
3. Multiply the mass in kilograms by c² to get the energy in joules
  $0.001 \times 8.987552e+16$ $= 89,875,517,873,681.77 J$
4. Change the answer to MeV, the unit you picked: divide by 1.602176634e-13
  $\frac{89,875,517,873,681.77}{1.602176634e-13}$ $= 5.6095886038e+26 MeV$
5. Equivalent mass: 1.64 oz
1. Change energy to J, the standard unit the formula uses (1 Mt TNT = 4.184e+15 J)
  $1 Mt TNT \times 4.184e+15$ $= 4.184e+15 J$
2. To find the mass, divide the energy by the speed of light squared (c = 299,792,458 m/s)
  $\frac{4.184e+15}{{299,792,458}^{2}}$ $= 0.046553278345 kg$
3. Change the answer to oz, the unit you picked: divide by 0.028349523125
  $\frac{0.046553278345}{0.028349523125}$ $= 1.64211856898 oz$
6. Equivalent mass: 93.11 g
1. Change energy to J, the standard unit the formula uses (1 Mt TNT = 4.184e+15 J)
  $2 Mt TNT \times 4.184e+15$ $= 8.368e+15 J$
2. To find the mass, divide the energy by the speed of light squared (c = 299,792,458 m/s)
  $\frac{8.368e+15}{{299,792,458}^{2}}$ $= 0.093106556691 kg$
3. Change the answer to g, the unit you picked: divide by 0.001
  $\frac{0.093106556691}{0.001}$ $= 93.106556690567 g$
7. Equivalent mass: 3.28 oz
1. Change energy to J, the standard unit the formula uses (1 Mt TNT = 4.184e+15 J)
  $2 Mt TNT \times 4.184e+15$ $= 8.368e+15 J$
2. To find the mass, divide the energy by the speed of light squared (c = 299,792,458 m/s)
  $\frac{8.368e+15}{{299,792,458}^{2}}$ $= 0.093106556691 kg$
3. Change the answer to oz, the unit you picked: divide by 0.028349523125
  $\frac{0.093106556691}{0.028349523125}$ $= 3.28423713796 oz$
8. Equivalent energy: 1.12e+33 eV
1. Change mass to kg, the standard unit the formula uses (1 g = 0.001 kg)
  $2 g \times 0.001$ $= 0.002 kg$
2. Square the speed of light (c), multiplying 299,792,458 m/s by itself
  ${299,792,458}^{2}$ $= 8.987552e+16 m²/s²$
3. Multiply the mass in kilograms by c² to get the energy in joules
  $0.002 \times 8.987552e+16$ $= 179,751,035,747,363.53 J$
4. Change the answer to eV, the unit you picked: divide by 1.602176634e-19
  $\frac{179,751,035,747,363.53}{1.602176634e-19}$ $= 1.1219177208e+33 eV$
9. Equivalent mass: 2.8e+25 Da
1. Change energy to J, the standard unit the formula uses (1 Mt TNT = 4.184e+15 J)
  $1 Mt TNT \times 4.184e+15$ $= 4.184e+15 J$
2. To find the mass, divide the energy by the speed of light squared (c = 299,792,458 m/s)
  $\frac{4.184e+15}{{299,792,458}^{2}}$ $= 0.046553278345 kg$
3. Change the answer to Da, the unit you picked: divide by 1.6605390689e-27
  $\frac{0.046553278345}{1.6605390689e-27}$ $= 2.8035039474e+25 Da$
10. Equivalent mass: 4.66e-5 t
1. Change energy to J, the standard unit the formula uses (1 Mt TNT = 4.184e+15 J)
  $1 Mt TNT \times 4.184e+15$ $= 4.184e+15 J$
2. To find the mass, divide the energy by the speed of light squared (c = 299,792,458 m/s)
  $\frac{4.184e+15}{{299,792,458}^{2}}$ $= 0.046553278345 kg$
3. Change the answer to t, the unit you picked: divide by 1,000
  $\frac{0.046553278345}{1,000}$ $= 0.000046553278 t$