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NEET PHYSICSEasy

The energy equivalent of 0.5 g of a substance is:

A

4.5 × 10^{13} J

B

1.5 × 10^{13} J

C

0.5 × 10^{13} J

D

4.5 × 10^{16} J

Step-by-Step Solution

  1. Formula: Einstein's mass-energy equivalence relation is given by: E=mc2E = mc^2 where EE is energy, mm is mass, and cc is the speed of light in vacuum (3×108 m/s3 \times 10^8 \text{ m/s}).
  2. Unit Conversion: The mass must be in SI units (kilograms). Given mass m=0.5 gm = 0.5 \text{ g}. m=0.5×10−3 kg=5×10−4 kgm = 0.5 \times 10^{-3} \text{ kg} = 5 \times 10^{-4} \text{ kg}
  3. Calculation: Substitute the values into the formula: E=(0.5×10−3 kg)×(3×108 m/s)2E = (0.5 \times 10^{-3} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 E=(0.5×10−3)×(9×1016)E = (0.5 \times 10^{-3}) \times (9 \times 10^{16}) E=4.5×1013 JE = 4.5 \times 10^{13} \text{ J}
  4. Conclusion: The energy equivalent is 4.5×10134.5 \times 10^{13} Joules.
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