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Physics: Nuclear Physics - Nuclear Fission and Fusion

Grade 8IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Nuclear Fission: The process where a heavy, unstable atomic nucleus, such as 92235U^{235}_{92}U, splits into two or more smaller, lighter nuclei. This process releases a significant amount of energy and extra neutrons.

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Chain Reaction: Neutrons produced during a fission event can strike other nearby nuclei, causing them to fission as well. In a nuclear reactor, this is controlled; in an atomic bomb, it is uncontrolled.

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Nuclear Fusion: The process where two light atomic nuclei (like isotopes of Hydrogen) combine to form a single heavier nucleus (like Helium). This process releases even more energy than fission and is the power source for stars like the Sun.

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Conditions for Fusion: Fusion requires extremely high temperatures (millions of degrees Celsius) and high pressure to overcome the electrostatic repulsion between the positively charged nuclei.

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Mass-Energy Equivalence: In both fission and fusion, the total mass of the products is slightly less than the mass of the original nuclei. This 'missing mass' (mass defect) is converted into energy according to Einstein's equation E=mc2E = mc^2.

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Radioactive Waste: Nuclear fission produces radioactive fragments that remain hazardous for thousands of years, whereas fusion produces much cleaner waste (mostly Helium).

📐Formulae

E=mc2E = mc^2

92235U+01n→56141Ba+3692Kr+301n+Energy_{92}^{235}U + _{0}^{1}n \rightarrow _{56}^{141}Ba + _{36}^{92}Kr + 3_{0}^{1}n + \text{Energy}

12H+13H→24He+01n+Energy_{1}^{2}H + _{1}^{3}H \rightarrow _{2}^{4}He + _{0}^{1}n + \text{Energy}

💡Examples

Problem 1:

Calculate the energy released if a nuclear reaction results in a mass loss of 2×10−5 kg2 \times 10^{-5}\text{ kg}. Take the speed of light c=3×108 m/sc = 3 \times 10^8\text{ m/s}.

Solution:

E=(2×10−5 kg)×(3×108 m/s)2E = (2 \times 10^{-5}\text{ kg}) \times (3 \times 10^8\text{ m/s})^2 E=2×10−5×9×1016E = 2 \times 10^{-5} \times 9 \times 10^{16} E=1.8×1012 JoulesE = 1.8 \times 10^{12}\text{ Joules}

Explanation:

Using Einstein's mass-energy equivalence formula E=mc2E = mc^2, we substitute the mass loss (mass defect) and the speed of light squared to find the energy in Joules.

Problem 2:

Identify the type of nuclear reaction shown below and explain why it is classified as such: 12H+12H→23He+01n_{1}^{2}H + _{1}^{2}H \rightarrow _{2}^{3}He + _{0}^{1}n

Solution:

This is a Nuclear Fusion reaction.

Explanation:

The reaction involves two light nuclei (Deuterium, 12H^{2}_{1}H) combining to form a heavier nucleus (Helium-3, 23He^{3}_{2}He). The combining of lighter nuclei into a heavier one is the definition of fusion.

Problem 3:

In a fission reaction of Uranium-235, if one neutron triggers the first split and each split releases 3 more neutrons, how many neutrons will be produced in the 3rd generation of the chain reaction?

Solution:

Generation 1: 31=3\text{Generation 1: } 3^1 = 3 Generation 2: 32=9\text{Generation 2: } 3^2 = 9 Generation 3: 33=27\text{Generation 3: } 3^3 = 27

Explanation:

In an uncontrolled chain reaction, the number of neutrons grows exponentially. If each nucleus releases 3 neutrons, the number of neutrons in generation nn is 3n3^n.