Question 475: Atoms & Nuclei

Question

A radioactive nucleus emits $$4 \alpha$$-particles and $$7 \beta$$-particles in succession. The ratio of number of neutrons of that of protons, is [$$A=$$ mass number, $$Z=$$ atomic number]

Accepted Answer

Let us assume, a particle $$X$$ having atomic number $$Z$$ and mass number $$A$$.
When an $$\alpha$$-particle is emitted by a nucleus, then its atomic number decreases by 2 and mass number decreases by 4. So, for given case,
$$z ^{X^A} \xrightarrow{4 \alpha 	ext {-particle }} z-8 ^{Y^{A-16}}$$
When a $$\beta$$-particle is emitted by a nucleus its atomic number increases by one and mass number remains unchanged. So, for given case,
$$Z-8 ^{Y^{A-16}} \xrightarrow{7 \beta 	ext {-particle }} Z-1 ^{Z^{A-16}}$$
$$\begin{aligned}
	herefore \frac{	ext { Number of neutrons }}{	ext { Number of protons }} & =\frac{(A-16)-(Z-1)}{(Z-1)} \
& =\frac{A-Z-15}{(Z-1)}
\end{aligned}$$

Answer

$$\frac{A-Z-13}{Z-2}$$

Answer

$$\frac{A-Z-15}{Z-1}$$

Answer

$$\frac{A-Z-13}{Z-1}$$

Answer

$$\frac{A-Z-11}{Z-2}$$

Atoms & Nuclei

A radioactive nucleus emits $4 \alpha-particles and 7 \beta-particles in succession. The ratio of number of neutrons of that of protons, is [A= mass number, Z=$ atomic number]

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