A radioactive sample of an isotope has a half-life of 20\text{ minutes}. If the initial ma… — JAMB UTME

A radioactive sample of an isotope has a half-life of $20\text{ minutes}$ . If the initial mass of the sample is $80\text{ g}$ , what mass of the isotope, in grams, will remain undecayed after $60\text{ minutes}$ ?

Answer: 10 g

Answer

10 g of the isotope remains undecayed.

The correct answer is derived from the half-life formula

N_t = N_0 \times (1/2)^n

. Since

60\text{ minutes}

contains three

20\text{ minute}

half-life periods (

n = 3

), the remaining mass is

80\text{ g} \times (1/2)^3 = 80\text{ g} / 8 = 10\text{ g}

Step-by-Step Solution

Determine the number of elapsed half-lives

3 half-lives

Divide the total time elapsed (

60\text{ minutes}

) by the duration of one half-life (

20\text{ minutes}

Calculate the remaining mass after 3 half-lives

10 g

Apply the radioactive decay relation

N_t = N_0 \times \left(\frac{1}{2}\right)^n

, yielding

80 \times \left(\frac{1}{2}\right)^3 = 10\text{ g}

Key Concept

Radioactive Half-Life and Exponential Decay

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