Question:

After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is

Updated On: Jun 14, 2022
  • 6000
  • 9000
  • 3000
  • 24000
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The Correct Option is D

Solution and Explanation

Activity reduces from 6000 dps to 3000 dps in 140 days. It implies that'half-life of the radioactive sample is 140 days. In 280 days (or two half-lives) activity will remain $\frac{1}{4}$ th of the initial activity. Hence, the initial activity of the sample is
$4\times6000 dps = 24000 dps$
Therefore, the correct option is (d).
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Concepts Used:

Decay Rate

The disintegration of unstable heavy atomic nuclei into lighter, more stable, atomic nuclei, accompanied in the process by the emission of ionizing radiation (alpha particles, beta particles or gamma rays). This is a random process at the atomic level but, given a large number of similar atoms, the decay rate on average is predictable, and is usually measured by the half-life of the substance.

The equation for finding out the decay rate is given below: