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: Using Einstein’s Mass-Energy Equivalence Formula Einstein’s famous equation relates mass and energy: \[ E = mc^2 \] where: 
- \( m = 3.2 \, \mu g = 3.2 \times 10^{-6} \, g = 3.2 \times 10^{-9} \, kg \), 
- \( c = 3 \times 10^8 \, m/s \) (speed of light in vacuum).

 Step 2: Calculating Energy in Joules \[ E = (3.2 \times 10^{-9}) \times (3 \times 10^8)^2 \] \[ E = (3.2 \times 10^{-9}) \times (9 \times 10^{16}) \] \[ E = 28.8 \times 10^7 \times 10^8 \] \[ E = 28.8 \times 10^{15} \, J \] 

Step 3: Converting to MeV Since \( 1 \, J = 6.242 \times 10^{12} \, MeV \), we convert: \[ E = (28.8 \times 10^{15}) \times (6.242 \times 10^{12}) \] \[ E = 1.8 \times 10^{21} \, MeV \] Rounding appropriately, we get: \[ E = 18 \times 10^{20} \, MeV \] Thus, the correct answer is \( \mathbf{(2)} \ 18 \times 10^{20} \, MeV \).