What happens to the (i) atomic number, (ii) mass number of the nucleus of an element when (a) an α particle, (b) a β particle, and (c) γ radiation, is emitted?

State whether the following nuclear disintegrations are allowed or not (star indicate an excited state). Give reason if it is not allowed.

(a) $_{Z}^{A}\text{X} \longrightarrow _{Z}^{A}\text{X} + \gamma$

(b) $_{Z}^{A}\text{X} \longrightarrow \space _{Z-2}^{ \space \space \space \space \space A}\text{X} + \space _{2}^{4}\text{He}$

Complete the following nuclear changes —

(a) $_{x}^{a}\text{P} \longrightarrow Q + _{-1}^{0}\text{β}$
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(b) $_{92}^{238}\text{U} \longrightarrow \space _{90}^{234}\text{Th} + …… + \text{energy}$

(c) $_{92}^{238}\text{P} \overset{\alpha} \longrightarrow \text{Q} \overset{\beta} \longrightarrow \text{R} \overset{\beta} \longrightarrow \text{S}$

(d) {Z}^{A}\text{X} \overset{\alpha} \longrightarrow \text{X}{1} \overset{\gamma} \longrightarrow \text{X}{2} \overset{2\beta} \longrightarrow \text{X}{3}

(e) $\text{X} \overset{\beta} \longrightarrow \text{X}${1} \overset{\alpha} \longrightarrow \text{X}{2} \overset{\alpha} \longrightarrow \space {69}^{172}\text{X}{3}

Why do we usually use isotopes emitting γ radiations as radioactive tracers in medical science?