Question

23 find the nuclear radius of $_{15}^{30}p$. a. 21.1 fm b. 5.9 fm c. 3.7 fm d. 10.3 fm e. 32.2 fm

Explanation:

Step1: Recall nuclear - radius formula

The formula for the nuclear radius is $R = R_0A^{\frac{1}{3}}$, where $R_0= 1.2\times10^{-15}\text{ m}=1.2\text{ fm}$ and $A$ is the mass number.

Step2: Identify the mass number

For the isotope $_{15}^{30}P$, the mass number $A = 30$.

Step3: Calculate the nuclear radius

Substitute $A = 30$ and $R_0=1.2\text{ fm}$ into the formula: $R=1.2\times30^{\frac{1}{3}}\text{ fm}$.
$30^{\frac{1}{3}}\approx3.107$, then $R = 1.2\times3.107\text{ fm}\approx3.7\text{ fm}$.

Answer:

C. 3.7 fm