The radius of nucleus of sliver (atomic number `= 47`) is `3.4 xx 10^(-14)m`. The electric potential on the surface of uncleus is `(e = 1.6 xx 10^(-19) C)`

Options

A. `1.99 xx 10^(6)` volt
B. `2.9 xx 10^(6)` volt
C. `4.99 xx 10^(6)` volt
D. `0.99 xx 10^(6)` volt

Explanation

To find the electric potential on the surface of the nucleus of silver, we will use the formula for electric potential \( V \) due to a point charge, which is given by:

\[ V = \frac{K \cdot Q}{R} \]

Where:
- \( V \) is the electric potential,
- \( K \) is Coulomb's constant (\( K \approx 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( Q \) is the total charge of the nucleus,
- \( R \) is the radius of the nucleus.

### Step 1: Determine the charge \( Q \) of the nucleus
The charge \( Q \) of the nucleus can be calculated using the atomic number \( Z \) (which is 47 for silver) and the elementary charge \( e \):

\[ Q = Z \cdot e = 47 \cdot (1.6 \times 10^{-19} \, \text{C}) \]

### Step 2: Calculate \( Q \)
Now, substituting the values:

\[ Q = 47 \cdot (1.6 \times 10^{-19}) = 75.2 \times 10^{-19} \, \text{C} = 7.52 \times 10^{-18} \, \text{C} \]

### Step 3: Use the radius \( R \) of the nucleus
The radius \( R \) of the nucleus is given as \( 3.4 \times 10^{-14} \, \text{m} \).

### Step 4: Substitute values into the potential formula
Now, substituting \( Q \) and \( R \) into the potential formula:

\[ V = \frac{K \cdot Q}{R} = \frac{(9 \times 10^9) \cdot (7.52 \times 10^{-18})}{3.4 \times 10^{-14}} \]

### Step 5: Calculate \( V \)
Calculating the above expression:

\[ V = \frac{(9 \times 10^9) \cdot (7.52 \times 10^{-18})}{3.4 \times 10^{-14}} \]

Calculating the numerator:

\[ 9 \times 10^9 \cdot 7.52 \times 10^{-18} = 67.68 \times 10^{-9} = 6.768 \times 10^{-8} \]

Now, dividing by \( 3.4 \times 10^{-14} \):

\[ V = \frac{6.768 \times 10^{-8}}{3.4 \times 10^{-14}} = 1.99 \times 10^6 \, \text{V} \]

### Final Answer
Thus, the electric potential on the surface of the nucleus of silver is:

\[ V \approx 1.99 \times 10^6 \, \text{V} \]