Nuclear reactions — balance and types of decay

How do you balance a nuclear reaction?

In every nuclear reaction the mass number $A$ (upper index) and the atomic number $Z$ (lower index) are conserved. The sums on both sides of the equation must match.

Nucleus notation and the general balance:

Types of decay:

In α decay the nucleus loses a ${}^{4}_{2}\text{He}$ particle. Beta decay is a transformation inside the nucleus: $\beta^-$ — neutron → proton + electron (Z increases by 1), $\beta^+$ — proton → neutron + positron (Z decreases by 1). In γ decay the nucleus merely radiates off excess energy — A and Z unchanged.

What penetrates the deepest?

The order of penetrating power is $\gamma > \beta > \alpha$: an α particle is stopped by a sheet of paper, β radiation by a few-millimetre aluminium plate, and γ radiation only by a thick layer of lead.

Why you need this for the exam:

Most nuclear-physics problems are balancing exercises: fill in the missing A and Z using the conservation of both numbers. Trick: write the upper indices separately and the lower ones separately — both sums must match.

Remember: in a nuclear reaction A and Z are conserved. α: (A−4, Z−2), β⁻: (A, Z+1), β⁺: (A, Z−1), γ: (A, Z). Penetration: γ > β > α.