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# A radioactive nucleus has a half-life of 20…

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## 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. 25,000particles
• D. 50,000particles

C

## DETAILS…

If the half-life = 20 years, it means at the end of every 20 years, half of the particles at the beginning would have decayed.

Therefore, at the end of 20 years, 100,000 particles would decay into 50,000 particles,

At the end of another 20 years, 50,000 particles would decay into 25,000 particles.

So, at the end of a total of 40 years, 75,000 particles would decay, and 25,000 would remain.

### Now for the right answer to the above question:

1. Option A is incorrect. 75,000 particles decayed, but 25,000 remained
2. Option B is incorrect.
3. C is correct.
4. D is not the correct answer. This should be the remnant after 20 years and not after 40 years.