A radioactive nucleus has a half-life of 20 years, starting with 100,000 particles, how many particles will be left exactly at the end of 40 years

  • A 75,000 particles
  • B 35,000 particles
  • C 25,000 particles
  • D 50,000 particles
jamb 2019chemistry

The correct answer is C. 25,000 particles

Given:

t\(_{\frac{1}{2}\) = 20 years

After the first 20 years, half of the substance (\(\frac{1}{2} \times 100,000 = 50,000\)) will have decayed. Hence, we have 100,000 - 50,000 = 50,000 particles left.

After the second 20 years (being 40 years in all), half of the remaining substance (\(\frac{1}{2} \times 50,000 = 25,000\)) will have decayed. 

Remaining particles after 40 years = 50,000 - 25,000

= 25,000 particles.

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