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
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Correct Answer: Option C
Explanation:
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.Â
Remaining particles after 40 years = 50,000 - 25,000
= 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.Â
Remaining particles after 40 years = 50,000 - 25,000
= 25,000 particles.