The energy equivalent to 1 amu is?

Options

A. `931.5 MeV`
B. `93.15 MeV`
C. `460 MeV`
D. `554 MeV`

Explanation

To find the energy equivalent to 1 atomic mass unit (amu), we can follow these steps:

### Step 1: Understand the mass of 1 amu
1 amu is defined as the mass of a proton, which is approximately \( 1.66 \times 10^{-27} \) kg.

### Step 2: Use Einstein's mass-energy equivalence formula
According to Einstein's equation, the energy (E) equivalent to a mass (m) is given by:
\[ E = mc^2 \]
where:
- \( m \) is the mass in kilograms,
- \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \) m/s.

### Step 3: Substitute values into the equation
Substituting the values into the equation:
\[ E = (1.66 \times 10^{-27} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2 \]

### Step 4: Calculate \( c^2 \)
Calculating \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]

### Step 5: Calculate the energy in joules
Now, substituting \( c^2 \) back into the equation:
\[ E = (1.66 \times 10^{-27}) \times (9 \times 10^{16}) \]
\[ E = 14.94 \times 10^{-11} \, \text{joules} \]

### Step 6: Convert joules to electron volts
To convert joules to electron volts, we use the conversion factor:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{joules} \]
Thus, we can find the energy in electron volts:
\[ E = \frac{14.94 \times 10^{-11}}{1.6 \times 10^{-19}} \, \text{eV} \]

### Step 7: Perform the division
Calculating the above expression:
\[ E \approx 933.75 \times 10^{6} \, \text{eV} = 933.75 \, \text{MeV} \]

### Conclusion
The energy equivalent to 1 amu is approximately \( 933.75 \, \text{MeV} \).

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