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NEET PHYSICSNUCLEIMedium

Question

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=0.4×107 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=0.4×107×109μg=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}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from NUCLEI. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSNUCLEIobtainedreactordisintegration

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