Calculate The Energy Released in The Following Fission Reaction

Nuclear fission is the process by which a heavy atomic nucleus splits into two or more lighter nuclei, releasing a large amount of energy. This energy can be calculated using the mass defect principle, which states that the energy released is equal to the difference in mass between the reactants and products, multiplied by the speed of light squared.

How to Calculate Energy Released in Fission

The energy released in a fission reaction can be calculated using the following steps:

Identify the mass of the parent nucleus (before fission)
Identify the masses of the daughter nuclei (after fission)
Calculate the mass defect (Δm) as the difference between the sum of daughter masses and the parent mass
Multiply the mass defect by the speed of light squared (c²) to get the energy released in joules

This calculation is based on Einstein's mass-energy equivalence principle, E = mc².

Fission Reaction Formula

The energy released in a fission reaction is calculated using the following formula:

E = (Δm) × c²

Where:

E = Energy released (Joules)
Δm = Mass defect (kilograms)
c = Speed of light (299,792,458 m/s)

The mass defect is calculated as:

Δm = (Sum of daughter masses) - (Parent mass)

Example Calculation

Consider the fission of uranium-235 (²³⁵U) into barium-141 (¹⁴¹Ba) and krypton-92 (⁹²Kr):

Mass of ²³⁵U = 235.0439299 u
Mass of ¹⁴¹Ba = 140.916929 u
Mass of ⁹²Kr = 91.92624 u

First, calculate the mass defect:

Δm = (140.916929 + 91.92624) - 235.0439299

Δm = 232.843169 - 235.0439299

Δm = -2.2007609 u

Convert the mass defect to kilograms (1 u = 1.66054 × 10⁻²⁷ kg):

Δm = -2.2007609 × 1.66054 × 10⁻²⁷ kg

Δm ≈ -3.667 × 10⁻²⁷ kg

Now calculate the energy released:

E = (-3.667 × 10⁻²⁷ kg) × (299,792,458 m/s)²

E ≈ -3.316 × 10⁻¹¹ J

The negative sign indicates energy release. The actual energy released is approximately 200 MeV per fission event.

Interpreting the Results

The energy released in fission reactions is typically measured in megaelectron volts (MeV) or joules. For practical purposes:

1 MeV ≈ 1.602 × 10⁻¹³ J
1 fission event releases about 200 MeV
This energy is used to produce electricity in nuclear power plants

Note: The actual energy released can vary depending on the specific fission reaction and the exact masses involved. The example above uses typical values for uranium-235 fission.

FAQ

What is the difference between fission and fusion?: Fission involves splitting heavy atomic nuclei, while fusion combines light nuclei to form heavier ones. Both processes release energy, but fission is currently more practical for power generation.
How is nuclear energy used in power plants?: In nuclear power plants, fission reactions generate heat that produces steam, which drives turbines to generate electricity. The heat is transferred to a working fluid that creates mechanical energy.
What are the environmental impacts of nuclear fission?: Nuclear fission produces radioactive waste that requires careful storage and disposal. While it emits less greenhouse gases than fossil fuels, it has other environmental and safety concerns.
Can nuclear fission be used for weapons?: Yes, nuclear weapons use controlled or uncontrolled fission reactions to release large amounts of energy in a short time, creating explosions. This is a dangerous application of the same physical principles.