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JEE Main levelNumerical answerDifficulty 2 of 3as179

The counting rate of a radioisotope falls from $800$ to $100$ counts per minute. Its decay constant is $0.0385 h^{- 1}$ . Use $ln 2 = 0.693$ . The time taken, in hours, to the nearest integer, is

Numerical answer type, answer in h, tolerance 1.

Answer: 54 h

800/100 = 8 = 2^{3}

, so

t = \frac{ln 8}{λ} = \frac{3 \times 0.693}{0.0385} = 54.0

h, i.e. 54 h to the nearest integer.

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