Question:
The radioisotope, tritium 13(H) has a half-life of 12.3 years. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 years:
The radioisotope, tritium 13(H) has a half-life of 12.3 years. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 years:
Updated On: Jul 26, 2024
1 mg
2 mg
4 mg
8 mg
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The Correct Option is B
Solution and Explanation
radioactive decay formula:
N(t) = N₀\(\times\)(\(\frac{1}{2}\))(\(\frac{t}{T}\))
Given,
N₀ = 32 mg
t = 49.2 years
T = 12.3 year
Put these values into the formula:
N(49.2) = 32 mg\(\times\)(\(\frac{1}{2}\)) (\(\frac{49.2}{12.3}\))
N(49.2) = 32 mg\(\times\)(\(\frac{1}{2}\))(4)
N(49.2) = 32 mg\(\times\)(\(\frac{1}{16}\))
N(49.2) = 2 mg
So, after 49.2 years, there would be 2 mg of tritium remaining.
The correct answer is (B) 2 mg.
N(t) = N₀\(\times\)(\(\frac{1}{2}\))(\(\frac{t}{T}\))
Given,
N₀ = 32 mg
t = 49.2 years
T = 12.3 year
Put these values into the formula:
N(49.2) = 32 mg\(\times\)(\(\frac{1}{2}\)) (\(\frac{49.2}{12.3}\))
N(49.2) = 32 mg\(\times\)(\(\frac{1}{2}\))(4)
N(49.2) = 32 mg\(\times\)(\(\frac{1}{16}\))
N(49.2) = 2 mg
So, after 49.2 years, there would be 2 mg of tritium remaining.
The correct answer is (B) 2 mg.
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