Nuclear Radius Calculation for $^{125}Sn$

This question asks for the approximate radius (R) of the nucleus $^{125}Sn$. We can estimate the nuclear radius using an empirical formula that relates the radius to the mass number (A) of the nucleus.

Nuclear Radius Formula

The radius R of a nucleus is commonly approximated using the formula:

$$R \approx R_0 \times A^{1/3}$$

Where:

• $R$ is the radius of the nucleus.
• $R_0$ is a constant, approximately $1.2 \ fm$ (femtometers). $1 \ fm = 10^{-15} \ m$.
• $A$ is the mass number of the nucleus.

Applying the Formula to $^{125}Sn$

For the nucleus $^{125}Sn$:

• The mass number $A = 125$.
• The constant $R_0 = 1.2 \ fm$.

Now, substitute these values into the formula:

$$R \approx 1.2 \ fm \times (125)^{1/3}$$

Step-by-Step Calculation

1. Calculate the cube root of A: Find the cube root of the mass number, $125$. $$(125)^{1/3} = \sqrt[3]{125} = 5$$
2. Multiply by $R_0$: Multiply the result by the constant $R_0$. $$R \approx 1.2 \ fm \times 5$$
3. Final Result: $$R \approx 6 \ fm$$

Conclusion

The approximate radius R of the $^{125}Sn$ nucleus is calculated to be $6 \ fm$. This value corresponds to one of the given options.