1 mg radium has 2.68 × 10 8 atoms. Its half-life is 1620 years. How many radium atoms will disintegrate from 1 mg of pure radium in 3240 years?

Question

1 mg radium has 2.68 × 10 8 atoms. Its half-life is 1620 years. How many radium atoms will disintegrate from 1 mg of pure radium in 3240 years?, 2.01 × 10 9, 2.01 × 10 8, 1.01 × 10 9, 1.01 × 10 8

MARKS App · Accepted Answer

Given that, the initial amount of radium N 0 = 1 mg and number of atoms in 1 mg radium = 2.68 × 10 8 atoms T 1 / 2 = 1620 years Number of half-lives n = T T 1 / 2 = 3240 1620 n = 2 ∴ Amount after 3240 years N = N 0 1 2 n = 1 1 2 2 N = 1 4 mg N = 1 4 × 2.68 × 10 8 atoms = 0.67 × 10 8 atoms ∴ Number of disintegrate atoms = 2.68 × 10 8 - 0.67 × 10 8 = 2.01 × 10 8

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