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The power obtained in a reactor using U-235 disintegration is 1000 kW. The mass decay of U-235 per hour is:

A

1 microgram

B

10 microgram

C

20 microgram

D

40 microgram

Step-by-Step Solution

  1. Identify Given Values:
  • Power (PP) = 1000 kW=1000×103 W=106 J/s1000 \text{ kW} = 1000 \times 10^3 \text{ W} = 10^6 \text{ J/s}.
  • Time (tt) = 1 hour = 3600 s3600 \text{ s}.
  • Speed of light (cc) ≈3×108 m/s\approx 3 \times 10^8 \text{ m/s} .
  1. Calculate Total Energy (EE):
  • Energy produced in 1 hour = Power ×\times Time.
  • E=106 J/s×3600 s=3.6×109 JE = 10^6 \text{ J/s} \times 3600 \text{ s} = 3.6 \times 10^9 \text{ J}.
  • Alternatively, using conversion factors: 1 kWh=3.6×106 J1 \text{ kWh} = 3.6 \times 10^6 \text{ J} . Energy = 1000 kWh=1000×3.6×106 J=3.6×109 J1000 \text{ kWh} = 1000 \times 3.6 \times 10^6 \text{ J} = 3.6 \times 10^9 \text{ J}.
  1. Apply Mass-Energy Equivalence:
  • According to Einstein's equation, E=Δmc2E = \Delta m c^2.
  • Mass decayed (Δm\Delta m) = E/c2E / c^2.
  • Δm=3.6×109 J(3×108 m/s)2=3.6×1099×1016 kg\Delta m = \frac{3.6 \times 10^9 \text{ J}}{(3 \times 10^8 \text{ m/s})^2} = \frac{3.6 \times 10^9}{9 \times 10^{16}} \text{ kg}.
  • Δm=0.4×10−7 kg\Delta m = 0.4 \times 10^{-7} \text{ kg}.
  1. Convert to Micrograms:
  • 1 kg=109 micrograms(μg)1 \text{ kg} = 10^9 \text{ micrograms} (\mu\text{g}).
  • Δm=0.4×10−7×109μg=0.4×100μg=40μg\Delta m = 0.4 \times 10^{-7} \times 10^9 \mu\text{g} = 0.4 \times 100 \mu\text{g} = 40 \mu\text{g}.
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