The mass number of atom whose nucleus has a radium of 5.6 Fermi `(R_0=1.40xx10^(-13)cm)` is

Options

A. 61
B. 37
C. 27
D. 64

Answer

To find the mass number of an atom whose nucleus has a radius of 5.6 Fermi, we can follow these steps:

### Step 1: Convert the radius from Fermi to cm
1 Fermi = \(10^{-13}\) cm. Therefore, we convert 5.6 Fermi to cm:
\[ 5.6 \text{ Fermi} = 5.6 \times 10^{-13} \text{ cm} \]

### Step 2: Use the formula for the radius of the nucleus
The radius \(r\) of a nucleus is related to its mass number \(A\) by the formula:
\[ r = R_0 A^{1/3} \]
where \(R_0\) is a constant approximately equal to \(1.4 \times 10^{-13} \text{ cm}\).

### Step 3: Rearrange the formula to solve for \(A\)
We can rearrange the formula to isolate \(A\):
\[ A^{1/3} = \frac{r}{R_0} \]
Cubing both sides gives:
\[ A = \left(\frac{r}{R_0}\right)^3 \]

### Step 4: Substitute the values of \(r\) and \(R_0\)
Substituting the values we have:
\[ A = \left(\frac{5.6 \times 10^{-13} \text{ cm}}{1.4 \times 10^{-13} \text{ cm}}\right)^3 \]

### Step 5: Simplify the fraction
Calculating the fraction:
\[ \frac{5.6}{1.4} = 4 \]
So we have:
\[ A = 4^3 \]

### Step 6: Calculate \(A\)
Calculating \(4^3\):
\[ A = 64 \]

### Final Answer
The mass number of the atom is \(A = 64\).

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