Question

If 10% of a radioactive material decay in 5 days, then the amount of original material left after 20 days is approximately :

Options

• 50

• 60

• 65

• 70

Answer 1

65

Explanation - 

N = N00e^-λt

When 10% decay N= 90%

So, 9 N₀ = N₀ `e^(-λ^5)`

⇒ log . 9 = -5λ       ...(i)

Let assume after 20 days fraction in decayed be x.

xN₀ = N₀ e - 20λ

log x = -20λ                       ... (ii)

from eqn (i) & (ii)

`1/4 = ("log".9)/("log" x)`

log x = 4 log . 9

x=(9)⁴ = 65

% of N = 65%