The electric potential at the surface of an atomic nucleus (Z = 50) of radius `9xx10^(-15)m` is

Options

A. `4xx10^(6)V`
B. `8xx10^(6)V`
C. `4xx10^(-6)V`
D. `8xx10^(-6)V`

Explanation

To find the electric potential at the surface of an atomic nucleus with atomic number \( Z = 50 \) and radius \( r = 9 \times 10^{-15} \, \text{m} \), we can use the formula for electric potential \( V \) due to a point charge:

\[ V = \frac{1}{4 \pi \epsilon_0} \frac{q}{r} \]

### Step 1: Calculate the charge \( q \) of the nucleus
The charge \( q \) of the nucleus can be calculated using the formula:

\[ q = Z \cdot e \]

where \( e \) is the elementary charge, approximately \( 1.6 \times 10^{-19} \, \text{C} \).

Substituting the values:

\[ q = 50 \cdot 1.6 \times 10^{-19} \, \text{C} = 80 \times 10^{-19} \, \text{C} = 8.0 \times 10^{-18} \, \text{C} \]

### Step 2: Substitute values into the electric potential formula
Now, substitute \( q \) and \( r \) into the electric potential formula. The value of \( 4 \pi \epsilon_0 \) is approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

\[ V = \frac{1}{4 \pi \epsilon_0} \frac{q}{r} = 9 \times 10^9 \cdot \frac{8.0 \times 10^{-18}}{9 \times 10^{-15}} \]

### Step 3: Simplify the expression
Now, simplify the expression:

\[ V = 9 \times 10^9 \cdot \frac{8.0}{9} \times 10^{-3} \]

### Step 4: Calculate the numerical value
Calculating the above expression:

\[ V = 9 \times 10^9 \cdot 8.0 \times 10^{-3} = 72 \times 10^6 \, \text{V} = 7.2 \times 10^7 \, \text{V} \]

### Step 5: Final result
Thus, the electric potential at the surface of the atomic nucleus is:

\[ V \approx 7.2 \times 10^7 \, \text{V} \]