The electric potential at the surface of an atmoic nucleus `(Z = 50)` of radius `9.0 xx 10^(-13) cm` is

Options

A. 80 V
B. `8 xx 10^(6) V`
C. 9 V
D. `9 xx 10 V`

Answer

To find the electric potential at the surface of an atomic nucleus with atomic number \( Z = 50 \) and radius \( 9.0 \times 10^{-13} \) cm, we can follow these steps:

### Step 1: Understand the formula for electric potential
The electric potential \( V \) at the surface of a charged sphere (like a nucleus) is given by the formula:
\[ V = \frac{k \cdot Q}{r} \]
where:
- \( V \) is the electric potential,
- \( k \) is Coulomb's constant (\( k \approx 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( Q \) is the total charge of the nucleus,
- \( r \) is the radius of the nucleus.

### Step 2: Calculate the total charge \( Q \)
The total charge \( Q \) of the nucleus can be calculated using the atomic number \( Z \):
\[ Q = Z \cdot e \]
where:
- \( e \) is the charge of a proton (\( e \approx 1.6 \times 10^{-19} \, \text{C} \)).
For \( Z = 50 \):
\[ Q = 50 \cdot (1.6 \times 10^{-19}) = 8.0 \times 10^{-18} \, \text{C} \]

### Step 3: Convert the radius to meters
The radius given is \( 9.0 \times 10^{-13} \) cm. We need to convert this to meters:
\[ r = 9.0 \times 10^{-13} \, \text{cm} = 9.0 \times 10^{-15} \, \text{m} \]

### Step 4: Substitute values into the potential formula
Now we can substitute the values of \( k \), \( Q \), and \( r \) into the formula:
\[ V = \frac{(8.99 \times 10^9) \cdot (8.0 \times 10^{-18})}{9.0 \times 10^{-15}} \]

### Step 5: Calculate the potential
Calculating the numerator:
\[ 8.99 \times 10^9 \cdot 8.0 \times 10^{-18} = 71.92 \times 10^{-9} = 7.192 \times 10^{-8} \, \text{V m} \]
Now divide by the radius:
\[ V = \frac{7.192 \times 10^{-8}}{9.0 \times 10^{-15}} \approx 7.991 \times 10^6 \, \text{V} \]
Thus, the electric potential at the surface of the nucleus is approximately:
\[ V \approx 7.99 \times 10^6 \, \text{V} \text{ or } 7.99 \, \text{MV} \]

### Final Answer
The electric potential at the surface of the atomic nucleus is approximately \( 7.99 \times 10^6 \, \text{V} \).

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