An isotope has an initial activity of 120 Bq. 6 days later its activity is

PHYSICS
JAMB 2022

An isotope has an initial activity of 120 Bq. 6 days later its activity is 15 Bq. The half-life is?

  • A. 3 day
  • B. 2 days
  • C. 1 day
  • D. 4 days

Correct Answer: A. 3 day

Explanation

The equation that establishes a relationship between the amountleft undecayed,

A, the initial amount, A0, and thenumber of half-lives that pass in a period of time t looks like this:

\(\frac{1}{2^n} * A_0 = A\)

\(\frac{1}{2^n} * 120 = 15\)

\(\frac{1}{2^n}\) = \(\frac{15}{120}\)

\(\frac{1}{2^n}\) = \(\frac{1}{8}\)

\(\frac{1}{2^n}\) = \(\frac{1}{2^3}\)

\(2^n = 2^3\)

n = 3



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