Question

How much time will have passed by the time a sample of an isotope has decayed to 6.25% of its original mass if the half-life is 15 days? 45 days 60 days 75 days 30 days

Answer 1

Answer:

60 days.

Explanation:

Let the original mass (N₀) = 1 g

Amount remaining (N) = 6.25% of its original mass

= 6.25% × 1

= 6.25/100 × 1

= 0.0625 g

Half life (t½) = 15 days

Time (t) =?

Next, we shall determine the rate of decay. This can be obtained as follow:

Decay constant (K) = 0.693/ half life

K = 0.693 / t½

Half life (t½) = 15 days

Decay constant (K) =?

K = 0.693 / t½

K = 0.693 / 15

K = 0.0462 / day

Finally, we shall determine the time taken for the sample of the isotope to decay to 6.25% of its original mass.

This can be obtained as follow:

Original amount (N₀) = 1 g

Amount remaining (N) = 0.0625 g

Decay constant (K) = 0.0462 / day

Time (t) =?

Log (N₀/N) = Kt/2.3

Log (1/0.0625) = 0.0462 × t / 2.3

Log 16 = 0.0462 × t / 2.3

1.2041 = 0.0462 × t /2.3

Cross multiply

0.0462 × t = 1.2041 × 2.3

Divide both side by 0.0462

t = (1.2041 × 2.3)/0.0462

t = 59.9 ≈ 60 days

Therefore, the time taken for the sample of the isotope to decay to 6.25% of its original mass is 60 days