The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is n × 10⁷ kWh, where n= __________. (speed of light =3 × 10⁸ m / s)

Solution

Physics sir · 3 steps

Turn the lost mass into joules with E = mc², then divide by the joules in one kWh.

1. Mass in kilograms. E = mc² gives joules only when the mass is in kilograms. So 0.4 g = 0.4 × 10⁻³ kg = 4 × 10⁻⁴ kg.

   E = mc² = (4 × 10⁻⁴)(3 × 10⁸)² = 3.6 × 10¹³ J

2. Joules to kWh. One kilowatt-hour is 1000 W × 3600 s = 3.6 × 10⁶ J. So E = (3.6 × 10¹³)/(3.6 × 10⁶) = 1 × 10⁷ kWh.
3. So. The energy liberated is 1 × 10⁷ kWh, so n = 1.

The common slip: 1000. Putting m = 0.4 in grams straight into E = mc² gives 1 × 10¹⁰ kWh, so n = 1000. Convert 0.4 g to 4 × 10⁻⁴ kg first.

The idea to keep. Mass defect to energy is always E = mc² with mass in kg, giving joules. For kWh, divide by 3.6 × 10⁶, since one kWh is a kilowatt running for 3600 seconds.

Answer from the NTA final answer key. Solution by PrepWiser.