Nuclear fission

In fission, a heavy nucleus such as uranium-235 absorbs a slow neutron, becomes unstable and splits into two smaller nuclei, releasing energy and two or three more neutrons. Those neutrons can split more nuclei in a chain reaction. A nuclear reactor keeps the chain reaction steady and uses the energy to make steam for its generators.

Key facts

  • Fission: a heavy nucleus splits into two smaller nuclei plus 2–3 neutrons, releasing energy.
  • A chain reaction happens when released neutrons cause further fissions; control rods absorb neutrons, the moderator slows them.
  • In a reactor, the energy from fission heats water into steam, which turns the turbines and generators.
  • Mass numbers and atomic numbers must balance on both sides of a nuclear equation.
  • E = mc² (c = 3.0 × 10⁸ m/s); 1 u of mass ≡ 931.5 MeV; 1 MeV = 1.6 × 10⁻¹³ J.
  • One fission of uranium-235 releases about 200 MeV, which is 3.2 × 10⁻¹¹ J.

Worked examples

Example 1

What starts a fission reaction in a nuclear reactor?

  1. A uranium-235 nucleus absorbs a slow neutron.
  2. It becomes very unstable.
  3. It splits in two, releasing energy and more neutrons.

Answer: a uranium-235 nucleus absorbing a neutron

Example 2

What is the job of the moderator in a nuclear reactor?

  1. Fission releases fast neutrons.
  2. Uranium-235 captures slow neutrons much better.
  3. The moderator (water or graphite) slows the neutrons so they cause more fission.

Answer: to slow down neutrons so they can cause more fission

Example 3

What is the job of the control rods in a nuclear reactor?

  1. Each fission releases neutrons that can cause more fissions.
  2. Control rods, made of a material such as boron, absorb neutrons.
  3. Pushing them in removes neutrons, so the chain reaction slows.

Answer: to absorb neutrons and control the rate of fission

Example 4

²³⁵U + ¹n → ¹⁴¹Ba + ⁹²Kr + x ¹n. Find x.

  1. Add the mass numbers on the left. 235 + 1 = 236
  2. Add the mass numbers on the right, leaving out the neutrons. 141 + 92 = 233
  3. The difference is the number of neutrons. x = 236 − 233 = 3

Answer: 3

Example 5

Uranium-235 absorbs a neutron and splits: ²³⁵U + ¹n → ¹⁴¹Ba + ⁹²Kr + neutrons. How many neutrons are released?

  1. Mass numbers must add up to the same total on both sides.
  2. Left: 235 + 1 = 236
  3. Right (without the neutrons): 141 + 92 = 233
  4. Each neutron has mass number 1: 236 − 233 = 3 neutrons

Answer: 3 neutrons

Example 6

In an uncontrolled chain reaction, each fission releases neutrons that cause 3 more fissions. Starting from 1 fission, how many fissions happen in generation 3 (the first fission is generation 1)?

  1. Each generation has 3 times as many fissions as the one before.
  2. Generation 3 is 2 steps after generation 1.
  3. 3^2 = 9 fissions

Answer: 9 fissions

Example 7

One uranium-235 fission releases about 200 MeV. Using 1 MeV = 1.6 × 10⁻¹³ J, how much energy is that, in units of 10⁻¹¹ J?

  1. Each MeV is 1.6 × 10⁻¹³ J.
  2. Multiply 200 MeV by this.
  3. 200 × 1.6 × 10⁻¹³ = 3.2 × 10⁻¹¹ J

Answer: 3.2 × 10⁻¹¹ J

Example 8

A 1,000 MW reactor gets 3.2 × 10⁻¹¹ J from each fission. How many fissions happen every second?

  1. Change the power to watts (joules each second). 1,000 MW = 1,000 × 10⁶ J/s
  2. Divide by the energy per fission. 1,000 × 10⁶ ÷ (3.2 × 10⁻¹¹) = 3.1 × 10¹⁹ per second

Answer: 3.1 × 10¹⁹

Example 9

In the reaction ²³⁵U + ¹n → ¹⁴¹Ba + ⁹²Kr + 3¹n, the mass lost is 0.18616 u. How much energy is released, in MeV, to 3 significant figures? (1 u = 931.5 MeV)

  1. The mass lost is 0.18616 u.
  2. Each u of mass is 931.5 MeV of energy.
  3. 0.18616 × 931.5 = 173.4 MeV

Answer: 173 MeV

Example 10

A reactor produces 500 MW of thermal power. Each fission releases 3.2 × 10⁻¹¹ J. How many fissions happen each second, in units of 10¹⁹, to 3 significant figures?

  1. 500 MW means 500 × 10⁶ J every second.
  2. Fissions per second = energy per second ÷ energy per fission.
  3. 500 × 10⁶ ÷ (3.2 × 10⁻¹¹) = 1.563 × 10¹⁹ per second
  4. = 1.56 × 10¹⁹

Answer: 1.56 × 10¹⁹