in a nuclear fission process, the mass defect was 1.2 x 10-5kg. Calculate the energy released. [speed of the light in vacuum = c = 3.0 x 108$ms^{-1}$]

Analyze the question

We are given the mass defect (Δm) in a nuclear fission process and asked to find the energy released. This is a direct application of Einstein's mass-energy equivalence.

Concept

Whenever mass is "lost" in a nuclear reaction, it is converted to energy:

E = Δm × c²

where

• Δm = mass defect (kg)
• c = speed of light = 3.0 × 10⁸ m/s
• E = energy released (J)

Solution

Δm = 1.2 × 10⁻⁵ kg (the question's "10-5" means 10⁻⁵) c² = (3.0 × 10⁸)² = 9.0 × 10¹⁶ m²/s²

E = (1.2 × 10⁻⁵) × (9.0 × 10¹⁶) E = 10.8 × 10¹¹ E = 1.08 × 10¹² J

Answer

The energy released is 1.08 × 10¹² J, which matches option C.

Tip

Multiply the numbers first, then add the powers of 10: 1.2 × 9 = 10.8, and −5 + 16 = 11. Then convert 10.8 × 10¹¹ to standard form (1.08 × 10¹²). Many students stop at 10.8 × 10¹¹ and wrongly pick A (1.08 × 10¹¹) because they slip on the decimal shift. Always check that your answer is in proper standard form before matching it to the options.