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:

• A. 1 mg
• B. 2 mg
• C. 4 mg
• D. 8 mg

Answer 1

Answer: (B)

2 mg

Answer 2

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.