Question 51: Atoms & Nuclei

Question

The mass number of two nuclei $$\mathrm{P}$$ and $$\mathrm{Q}$$ are 27 and 125 respectively. The ratio of their radii $$R_P: R_Q$$ is given by:

Accepted Answer

To find the ratio of the radii $$R_P : R_Q$$ of two nuclei with mass numbers $$A_P = 27$$ and $$A_Q = 125$$ respectively, we use the empirical formula for the radius of a nucleus, which is given by:
$R = R_0 A^{1/3}$
where $R$ is the radius, $A$ is the mass number of the nucleus, and $R_0$ is a constant. Using this formula, we can express the radii of nuclei P and Q as:
$R_P = R_0 A_P^{1/3}$
$R_Q = R_0 A_Q^{1/3}$
To find the ratio $R_P : R_Q$, we divide the expression for $R_P$ by the expression for $R_Q$:
$\frac{R_P}{R_Q} = \frac{R_0 A_P^{1/3}}{R_0 A_Q^{1/3}} = \frac{A_P^{1/3}}{A_Q^{1/3}}$
Substituting the given values of $A_P = 27$ and $A_Q = 125$, we get:
$\frac{R_P}{R_Q} = \frac{27^{1/3}}{125^{1/3}}$
Since $27 = 3^3$ and $125 = 5^3$, the expression simplifies to:
$\frac{R_P}{R_Q} = \frac{3}{5}$
Therefore, the ratio of their radii $R_P : R_Q$ is $3 : 5$, which corresponds to Option B.

Answer

9 : 25

Answer

3 : 5

Answer

27 : 25

Answer

5 : 3

Atoms & Nuclei

The mass number of two nuclei $\mathrm{P} and \mathrm{Q} are 27 and 125 respectively. The ratio of their radii R_P: R_Q$ is given by:

Choose the correct answer: