Question

What do you mean by nuclear reaction? What quantities are conserved in nuclear reaction? What is Q-value of nuclear reaction?

Answer 1

Nuclear Reaction

The conversion of the nucleus of an element into a nucleus of another element is called a nuclear reaction. This is generally caused by bombarding the target nucleus by high energy particle.

For example, if an incident projectile ‘a’ hits the target nucleus X, a nuclear reaction takes place and as a result there is a new nucleus Y and an outgoing particle ‘b’ are produced.

i.e. a + X → Y + b

In short form, this reaction can be written as X (a,b) Y.

In 1919, Rutherford observed that when α-particles, from a polonium source were made to hit nitrogen atom, protons were given off in the reaction. The nuclear reaction for this process can be written as

₇N¹⁴ + ₂He⁴ → ₈O¹⁷ + H¹

The above reaction can also be written as ₇N¹⁴ (α,p) ₈O¹⁷.

Following quantities remain conserved during a nuclear reaction.

1. Conservation of charge. Total charge of the reactant is conserved.
2. Conservation of nucleons. Total number of nucleons before and after the reaction remains constant.
3.  Mass and energy conservation. In a nuclear reaction mass and energy are not separately conserved. However, their total is always conserved i.e. the energy equivalent of mass is liberated as can be understood in the Q-value of the nuclear reactions.
4. Conservation of linear momentum. It is a fundamental law and is always conserved in nuclear reactions also.
5. Conservation of angular momentum. Total angular momentum J is composed of orbital angular momentum L and spin angular momentum S. Vector sum of the total angular momentum is conserved in a nuclear reaction.

Q-Value of a nuclear reaction

Consider a nuclear reaction represented by the equation

a + x → y + b

where target nucleus ‘x’ is supposed to be at rest initially. Since the total energy of the system is to be conserved. Let the mass of projectile ‘a’, target nucleus x, product nucleus y and product particle ‘b' be represented as ma, Mx, My and ma respectively. Then from the law of conservation of total energy, we have

(E_a + m_ac²) + M_xc² = (E_y + M_yc²) + (E_b + m_p c²) ..........(1)

Where E’s correspond to the kinetic energies. Let us introduce a quantity called Q-value of the nuclear reaction, which represents the difference of energy of the products and the reactants.

i.e. Q = E_y + E_b - E_a

So Eq. (1) may take the form

(m_a + M_x - M_y - m_b) c² 

= E_y + E_b - E_a = Q

or Q = [(m_a +M_x) - (M_y + m_b)] c²

Thus Q-value of a nuclear reaction is defined as the energy available from the difference in mass of the projectile plus the target and the product nucleus and the product particle.

If (m_a + M_x) > (M_y + m_b), then Q > 0 and the reaction releases energy called exoergic reaction. If (m_a + M_x) < (m_y + m_b), then Q < 0 and the reaction absorb energy and called endoergic reaction.