Question

The energy equivalent of 1 g of a substance in joules is:

• A. \( 9 \times 10^{13} \)
• B. \( 4.5 \times 10^{13} \)
• C. \( 1 \times 10^{13} \)
• D. \( 0.5 \times 10^{13} \)
• E. \( 2.25 \times 10^{13} \)

Hint:

The energy equivalent of mass is given by \( E = mc^2 \), where \( c = 3 \times 10^8 \, {m/s} \) is the speed of light.

Answer 1

The Correct Option is A

Step 1: The energy equivalent \( E \) of mass \( m \) is given by Einstein's equation: \[ E = mc^2 \] 
where: 
- \( m = 1 \, {g} = 1 \times 10^{-3} \, {kg} \), 
- \( c = 3 \times 10^8 \, {m/s} \). 
Step 2: Substitute the values into the equation: \[ E = (1 \times 10^{-3}) \times (3 \times 10^8)^2 = 9 \times 10^{13} \, {J} \] 
Thus, the energy equivalent of 1 g of substance is \( 9 \times 10^{13} \, {J} \).