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Electricity generation is essential for modern life, and various methods exist to convert natural energy sources into electrical power. Among these, nuclear power stands out as a highly efficient and reliable source of energy. It harnesses the energy stored in the nucleus of atoms, unlike thermal or hydroelectric plants that rely on burning fuel or water flow.
In India, nuclear power contributes significantly to the energy mix, providing a stable supply of electricity with low greenhouse gas emissions. Globally, nuclear power plants supply about 10% of the world's electricity, demonstrating their importance in meeting energy demands sustainably.
The fundamental process behind nuclear power is nuclear fission, where heavy atomic nuclei split into smaller parts, releasing a tremendous amount of energy. This energy is then converted into heat to produce steam, which drives turbines connected to generators, producing electricity.
Compared to fossil fuel-based thermal plants, nuclear power offers advantages such as higher energy density, lower fuel consumption, and reduced air pollution. However, it also presents challenges like radioactive waste management and stringent safety requirements.
To understand nuclear power, we must first grasp the concept of nuclear fission. This is a nuclear reaction where the nucleus of a heavy atom, such as Uranium-235 (\(^{235}U\)), splits into two smaller nuclei, along with a few free neutrons and a large amount of energy.
Here is how the process works:
The emitted neutrons can then collide with other Uranium-235 nuclei, causing them to split as well. This creates a chain reaction, where one fission event leads to multiple others, sustaining a continuous release of energy.
To control this chain reaction, nuclear reactors use:
Nuclear reactors are specially designed systems that maintain and control the nuclear fission chain reaction to produce heat safely and efficiently. Several types of reactors are used worldwide, each with unique features suited to different operational needs.
Here are the most common types of reactors used in power generation:
The PWR is the most widely used reactor type globally. It uses water as both a coolant and a moderator. The water in the reactor core is kept under high pressure to prevent it from boiling, even at high temperatures.
In a BWR, water acts as coolant and moderator but is allowed to boil inside the reactor vessel itself.
FBRs use fast neutrons (without moderators) to sustain the chain reaction. They "breed" more fissile material than they consume by converting fertile isotopes (like Uranium-238) into fissile Plutonium-239.
graph TD A[Reactor Core] --> B[Heat Generation by Fission] B --> C[Primary Coolant Loop] C --> D[Heat Exchanger] D --> E[Secondary Coolant Loop] E --> F[Steam Generation] F --> G[Turbine] G --> H[Electric Generator] A --> I[Control Rods (Neutron Absorption)] A --> J[Moderator (Neutron Slowing)]
Step 1: Determine the number of Uranium-235 atoms in 1 gram.
The molar mass of Uranium-235 is 235 g/mol.
Number of moles in 1 g = \(\frac{1}{235} = 0.004255\) mol
Number of atoms \(N = 0.004255 \times 6.022 \times 10^{23} = 2.56 \times 10^{21}\) atoms
Step 2: Calculate total mass defect.
Mass defect per fission = \(0.2 \times 10^{-27}\) kg
Total mass defect = \(2.56 \times 10^{21} \times 0.2 \times 10^{-27} = 5.12 \times 10^{-7}\) kg
Step 3: Use Einstein's mass-energy equivalence formula:
\[ E = \Delta m \times c^2 \]
where \(c = 3 \times 10^8\) m/s
\[ E = 5.12 \times 10^{-7} \times (3 \times 10^8)^2 = 5.12 \times 10^{-7} \times 9 \times 10^{16} = 4.61 \times 10^{10} \text{ Joules} \]
Answer: Approximately \(4.6 \times 10^{10}\) Joules of energy is released from 1 gram of Uranium-235 fission.
Step 1: Calculate total annual cost.
Assuming capital cost is amortized over 30 years:
Annual capital cost = \(\frac{12,000 \text{ crores}}{30} = 400 \text{ crores}\)
Total annual cost = 400 + 600 = 1000 crores
Step 2: Calculate cost per kWh.
Total energy generated = 8,000 million kWh = \(8 \times 10^9\) kWh
Cost per kWh = \(\frac{1000 \times 10^7 \text{ INR}}{8 \times 10^9 \text{ kWh}} = \frac{10^{10}}{8 \times 10^9} = 1.25 \text{ INR/kWh}\)
Answer: The cost of electricity generation is Rs.1.25 per kWh.
Step 1: Calculate electrical output of nuclear plant.
\(P_{out} = \eta \times P_{in} = 0.33 \times 3000 = 990 \text{ MW}\)
Step 2: Calculate electrical output of thermal plant.
\(P_{out} = 0.30 \times 3000 = 900 \text{ MW}\)
Answer: The nuclear plant produces 990 MW, which is 90 MW more than the thermal plant.
Step 1: Calculate total neutrons produced by 100 fissions.
Total neutrons = \(100 \times 2.5 = 250\)
Step 2: Neutrons needed to sustain chain reaction = 1 neutron per fission x 100 fissions = 100 neutrons
Step 3: Neutrons to be absorbed or lost = \(250 - 100 = 150\)
Answer: Control rods and other means must absorb 150 neutrons per 100 fissions to keep the reaction steady.
Step 1: Calculate the number of half-lives elapsed.
\(n = \frac{t}{T_{1/2}} = \frac{72,000}{24,000} = 3\)
Step 2: Use the radioactive decay formula:
\[ N = N_0 \times \left(\frac{1}{2}\right)^n \]
\(N = 1000 \times \left(\frac{1}{2}\right)^3 = 1000 \times \frac{1}{8} = 125 \text{ kg}\)
Answer: After 72,000 years, 125 kg of the isotope remains.
When to use: When calculating energy released from small mass defects in nuclear reactions.
When to use: While solving numerical problems involving power plant economics and efficiency.
When to use: When solving radioactive decay and nuclear waste management questions.
When to use: When studying reactor control and neutron economy.
When to use: During multiple-choice questions involving advantages and disadvantages.
| Feature | Nuclear Power | Thermal Power | Hydroelectric Power | Solar Power |
|---|---|---|---|---|
| Efficiency | 33-37% | 30-35% | 35-45% | 15-20% |
| Fuel Availability | Uranium (limited) | Coal (abundant) | Water (renewable) | Sunlight (renewable) |
| Environmental Impact | Low emissions, radioactive waste | High emissions, pollution | Low emissions, ecological impact | No emissions, land use |
| Cost per kWh | Rs.1-3 | Rs.2-5 | Rs.1-3 | Rs.3-6 |
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