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NEET PHYSICSMedium

10 g of radioactive material of half-life 15 year is kept in store for 20 years. The disintegrated material mass is

A

12.5 g

B

10.5 g

C

6.03 g

D

4.03 g

Step-by-Step Solution

  1. Identify Given Values:
  • Initial mass (N0N_0) = 10 g
  • Half-life (T1/2T_{1/2}) = 15 years
  • Time elapsed (tt) = 20 years
  1. Calculate Remaining Mass (NN):
  • The formula for the remaining amount of a radioactive substance is N=N0(12)t/T1/2N = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}} .
  • Substitute the values: N=10(12)20/15=10(12)4/3N = 10 \left(\frac{1}{2}\right)^{20/15} = 10 \left(\frac{1}{2}\right)^{4/3}.
  • Calculation: (12)1.333≈0.3968\left(\frac{1}{2}\right)^{1.333} \approx 0.3968.
  • N≈10×0.3968=3.97N \approx 10 \times 0.3968 = 3.97 g.
  1. Calculate Disintegrated Mass:
  • The question asks for the mass that has disintegrated (decayed), not the remaining mass.
  • Disintegrated Mass = Initial Mass - Remaining Mass.
  • Disintegrated Mass = 10 g−3.97 g=6.03 g10 \text{ g} - 3.97 \text{ g} = 6.03 \text{ g}.
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