Question

Sodium-24 has a half-life of 15 hours. When will 4 mg of Sodium-24 remain if the original sample contains 64 mg?

Answer 1

60 hours

Explanation:

We are given;

Initial amount: A_o = 64 mg

Half life; T_½ = 15 hours

Amount left: A = 4 mg

To get the time that 4 mg of Sodium-24 remain, we will use the formula;

A = A_o(½^(t/T_½))

Where t is the time that 4 mg of Sodium-24 remain.

Thus;

4 = 64 × ½^(t/15)

Divide both sides by 64 to get;

4/64 = 2^(t/15)

0.0625 = ½^(t/15)

In 0.0625 = (t/15) In 0.5

-2.7726 = (t/15) × -0.6931

t = (-2.7726 × 15)/-0.6931

t = 60 hours