Conservation of Mass and Energy
Mass–energy equivalence, binding energy, and nuclear reactions
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Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. According to conservation of mass and energy, matter…
2. How much energy is obtained by converting 2.0 kg of mass completely into energy? (c = 3.00 × 10⁸ m/s)
3. How much energy is released when 2 universal mass units are completely converted to energy? (1 u = 931 MeV)
4. A neutron splits a uranium nucleus into smaller nuclei. This reaction is called…
5. Why can a small amount of mass release a huge amount of energy?
Mass Into Energy
Einstein’s equation E = mc² shows that mass and energy are equivalent. (c = 3.00 × 108 m/s; 1 u = 931 MeV)
How much energy is equivalent to 1.0 gram (0.0010 kg) of mass?
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C1. When a deuteron forms from a proton and a neutron, the deuteron’s mass is 0.0024 u less than the separate particles. How much energy is released?
C2. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C3. A nuclear power plant produces 1.0 × 109 W of power for one day (8.64 × 104 s). Substitute numerical values into a mathematical representation that can be used to determine the mass converted to energy in one day (assume 100% efficiency). Then calculate the mass.
C4. The mass of a helium-4 nucleus is 0.0304 u less than the total mass of its two protons and two neutrons. Determine the binding energy of the helium-4 nucleus.
C5. An electron (rest energy 0.511 MeV) and a positron annihilate at rest. What total energy is released as photons?
C6. Burning 1.0 kg of coal releases about 3 × 107 J, while fission of 1.0 kg of uranium-235 releases about 8 × 1013 J. Using E = mc2, compare the mass converted in each case, and identify one benefit and one drawback of nuclear power compared with coal.