Read the given statements and select the correct option.
Statement 1 : 1 atomic mass unit is equivalent to about 931 mega electron volts of energy.
Statement 2: 1 electron volt = `1.602 xx 10^(-13)` joule

Options

A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true but statement 2 is false.
D. Both statements 1 and 2 are false.

Answer

To solve the question, we need to evaluate the two statements provided and determine their correctness.

**Step 1: Evaluate Statement 1**
- Statement 1 claims that 1 atomic mass unit (amu) is equivalent to about 931 mega electron volts (MeV) of energy.
- According to Einstein's mass-energy equivalence principle, the energy (E) can be calculated using the formula:
\[ E = mc^2 \]
where \(m\) is the mass in kilograms and \(c\) is the speed of light in a vacuum (\(c \approx 3 \times 10^8 \, \text{m/s}\)).
- The mass of 1 amu is approximately \(1.66 \times 10^{-27} \, \text{kg}\).

Calculating the energy:
\[ E = (1.66 \times 10^{-27} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2 \]
\[ E = (1.66 \times 10^{-27}) \times (9 \times 10^{16}) \approx 1.494 \times 10^{-10} \, \text{J} \]

Now, converting joules to electron volts:
- 1 electron volt (eV) = \(1.602 \times 10^{-19} \, \text{J}\)
\[ E \text{ in eV} = \frac{1.494 \times 10^{-10}}{1.602 \times 10^{-19}} \approx 931 \, \text{MeV} \]
Thus, Statement 1 is correct.

**Step 2: Evaluate Statement 2**
- Statement 2 states that 1 electron volt = \(1.602 \times 10^{-13} \, \text{J}\).
- However, the correct value is \(1.602 \times 10^{-19} \, \text{J}\).
- Therefore, Statement 2 is incorrect.

**Conclusion:**
- Statement 1 is correct.
- Statement 2 is incorrect.

The correct option based on the evaluation is:
- Only Statement 1 is true.