Question

An atomic nucleus A is composed of 84 protons and 128 neutrons.

1. The nucleus A emits a beta particle and is transformed into nucleus B. What is the composition of nucleus of B?
2. The nucleus B emits an α-particle and is transformed into nucleus C. What is the composition of nucleus C?
3. Does the composition of nucleus C change if it emits a γ-radiation?

Answer 1

Let nucleus A have atomic number Z = 84 and mass number A = 84 + 128 = 212.

(a) Beta decay: A neutron converts into a proton and emits an electron. The mass number remains unchanged, but the atomic number increases by 1.

\[ {}^{212}_{84}\mathrm{A} \longrightarrow {}^{212}_{85}\mathrm{B} + {}^{\phantom{-}0}_{-1}e \]

So nucleus B contains 85 protons and 128 − 1 = 127 neutrons.

(b) Alpha decay: Nucleus B loses an alpha particle (2 protons + 2 neutrons), so the atomic number decreases by 2 and the mass number decreases by 4.

\[ {}^{212}_{85}\mathrm{B} \longrightarrow {}^{208}_{83}\mathrm{C} + {}^{4}_{2}\mathrm{He} \]

So nucleus C contains 83 protons and 127 − 2 = 125 neutrons.

(c) No. Gamma radiation is pure electromagnetic energy emitted by an excited nucleus; it carries no charge and changes neither the number of protons nor neutrons. Therefore, nucleus C remains 83 protons and 125 neutrons.