Question

A radioactive isotope has a half life of 5 years. How long will it take the activity to reduce to 3.125%?

Answer 1

Let the number of half life is n
You should use the formula,
$\bold{\frac{N}{N_0}=\frac{1}{2^n}}$ ------(1)

But according to question,
N/N₀ = 3.125 = 3125/100000 = 1/32 = 1/2⁵

Now, from equation (1)
N/N₀ = 1/2⁵ = 1/2ⁿ ⇒ n = 5
hence, there are 5 half life so, life of radioactive substance = 5 × one half life
= 5 × 5 = 25 years

Answer is 25 years