Class 12 > Unit # 27: Nuclear Physics > Nuclear Reactions

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Nuclear Reactions, Energy Released & Conservation Laws

27.4 Nuclear Reactions

Any process that involves a change in the nucleus of an atom is called a nuclear reaction.

Mathematically, it is represented as:

$X + x \to Y + y + Q$

Where:

• $X$ is the target nucleus,
• $x$ are the projectiles,
• $y$ are the ejectiles, and
• $Y$ is called the residual (product) nucleus.

27.4.1 Energy Released from Nuclear Reactions

The energy that is either absorbed or emitted is called the Q value, and it is equal to the mass defect.

The Q value can also be defined as the difference between the rest energies of $X$ and $x$ and the rest energies of $Y$ and $y$:

$Q = (m_X + m_x - m_Y - m_y)c^2$

The value of $Q$ is taken as positive when energy is released, and its corresponding reaction is called exothermic. Similarly, the value of $Q$ is taken as negative when energy is absorbed, and its corresponding reaction is called endothermic.

27.4.2 Conservation of Atomic and Mass Numbers

Whenever there is a nuclear decay, there are always some physical quantities that need to be conserved or remain constant. The following are rules for any nuclear reaction:

1. The total of the atomic numbers ($Z$) on the left is the same as the total on the right of the given equation because charge must be conserved.
2. The total of the mass numbers ($A$) on the left is the same as the total on the right of the equation because nucleon number must be conserved.

For example, in the following nuclear reaction, the total atomic number and mass number remain the same on both sides of the equation:

$^{A}_{Z}X = {}^{238}_{\ 92}\text{U} \to {}^{234}_{\ 90}\text{Th} + {}^{4}_{2}\text{He}$

In the above reaction, $Z = 92$ on the left side, which is equal to $90 + 2 = 92$ on the right side. Similarly, $A = 238$ on the left side, which is equal to $234 + 4 = 238$ on the right side.

27.4.3 Conservation of Mass and Energy

According to Einstein's mass-energy relationship ($E = mc^2$), in all nuclear reactions, the total sum of mass and energy must be conserved. This means the total mass on the left side of the equation (before the decay) is equal to the total mass on the right side (after the decay), plus the Q value.

The Q value represents the mass difference before and after the decay, and this difference is converted into energy according to the mass-energy relationship ($E = mc^2$). This released energy is typically in the form of kinetic energy of the decay products, such as alpha particles, beta particles, or gamma rays.

So, the equation that represents the conservation of mass and energy in radioactive decay can be expressed as:

Total mass before decay = Total mass after decay + Q-value

This equation underscores the principle that while mass may appear to decrease due to the emission of particles, the lost mass is accounted for in the form of energy released during the decay process.

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