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CUET · PHYSICS · PYQ PAPER 2023

The half life of \( U^{238} \) when 1 gram of it emits \( 1.23 \times 10^4 \) alpha particle per second is : (taking 1 year = \( 3.155 \times 10^7 \) second)

  1. A \( 1.84 \times 10^8 \) years
  2. B \( 2.413 \times 10^9 \) years
  3. C \( 4.519 \times 10^9 \) years
  4. D \( 6.2 \times 10^7 \) years
Verified Solution

Answer & Solution

Correct Answer

(C) \( 4.519 \times 10^9 \) years

Step-by-step Solution

Detailed explanation

\(N = \frac{1 \text{ g}}{238 \text{ g/mol}} \times 6.022 \times 10^{23} \text{ mol}^{-1} = 2.53865 \times 10^{21}\) \(\lambda = \frac{1.23 \times 10^4 \text{ s}^{-1}}{2.53865 \times 10^{21}} = 4.8459 \times 10^{-18} \text{ s}^{-1}\)…