Question

The energy equivalent of \(3.2 \, \mu g\) of mass is

• A. \(18 \times 10^{26} \, J\)
• B. \(18 \times 10^{20} \, MeV\)
• C. \(18 \times 10^{23} \, MeV\)
• D. \(32 \times 10^{26} \, J\)

Hint:

Einstein’s equation \( E = mc^2 \) is used to calculate the energy equivalent of mass. Always ensure proper unit conversion, especially from Joules to MeV using: \[ 1 \, J = 6.242 \times 10^{12} \, MeV \]

Answer 1

The Correct Option is B

Step 1: Mass–energy relation

\[ E = mc^2 \]

\[ m = 3.2 \,\mu\text{g} = 3.2 \times 10^{-9} \, \text{kg}, \quad c = 3 \times 10^8 \, \text{m/s} \]

Step 2: Energy in joules

\[ E = (3.2 \times 10^{-9})(3 \times 10^8)^2 \]

\[ E = (3.2 \times 10^{-9})(9 \times 10^{16}) \]

\[ E = 28.8 \times 10^{7} \, \text{J} = 2.88 \times 10^{8} \, \text{J} \]

Step 3: Convert to MeV

\[ 1 \, \text{J} = 6.242 \times 10^{12} \, \text{MeV} \]

\[ E = (2.88 \times 10^{8})(6.242 \times 10^{12}) \]

\[ E \approx 1.8 \times 10^{21} \, \text{MeV} \]

\[ E = 18 \times 10^{20} \, \text{MeV} \]

Final Answer: \( 18 \times 10^{20} \, \text{MeV} \)