If `4 xx 10^(20)eV` energy is required to move a charge of `0.25` coulomb between two points. Then what will be the potential difference between them ?

Options

A. `178 V`
B. `256 V`
C. `356 V`
D. None of these

Explanation

To find the potential difference between two points when a charge is moved, we can use the formula:

\[ V = \frac{W}{Q} \]

where:
- \( V \) is the potential difference (in volts),
- \( W \) is the work done or energy required (in joules),
- \( Q \) is the charge (in coulombs).

### Step 1: Convert Energy from eV to Joules
The energy given is in electron volts (eV). We need to convert this energy into joules. The conversion factor is:

\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]

So, we can convert \( 4 \times 10^{20} \text{ eV} \) to joules:

\[ W = 4 \times 10^{20} \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} \]

Calculating this gives:

\[ W = 4 \times 1.6 \times 10^{1} \text{ J} = 6.4 \times 10^{1} \text{ J} = 64 \text{ J} \]

### Step 2: Use the Formula to Find Potential Difference
Now that we have the work done in joules, we can substitute \( W \) and \( Q \) into the formula for potential difference:

\[ V = \frac{W}{Q} = \frac{64 \text{ J}}{0.25 \text{ C}} \]

Calculating this gives:

\[ V = 64 \div 0.25 = 256 \text{ V} \]

### Final Answer
The potential difference between the two points is:

\[ \boxed{256 \text{ V}} \]