Question

The energy equivalent of 5 g of a substance is

• A. 4.5×10¹²j
• B. 9×10¹²j
• C. 4.5×10¹⁴j
• D. 4.5×10¹⁶j
• E. 9×10¹⁶j

Answer 1

The Correct Option is C

The energy equivalent of a substance can be found using Einstein's famous equation: \[ E = mc^2 \] where:
\( E \) is the energy,
\( m \) is the mass of the substance,
\( c \) is the speed of light (\( c = 3 \times 10^8 \, \text{m/s} \)).

Given:
\( m = 5 \, \text{g} = 5 \times 10^{-3} \, \text{kg} \).
Now, using the formula: \[ E = (5 \times 10^{-3}) \times (3 \times 10^8)^2 \] \[ E = 5 \times 10^{-3} \times 9 \times 10^{16} \] \[ E = 4.5 \times 10^{14} \, \text{J} \] Thus, the energy equivalent of 5 g of the substance is \( 4.5 \times 10^{14} \, \text{J} \).

The correct option is (C) : \(4.5×10^{14}\ J\)

Answer 2

To find the energy equivalent of a mass, we use Einstein’s mass-energy equivalence relation: 
 
E = mc² 

Given:

• m = 5 g = 5 × 10^-3 kg
• c = 3 × 10⁸ m/s

Now,
E = (5 × 10^-3) × (3 × 10⁸)² 
= (5 × 10^-3) × (9 × 10¹⁶) 
= 4.5 × 10¹⁴ joules 

✅ Correct Option: 4.5 × 10¹⁴ J