Question

A radioactive material is reduced to 1/16 of its original amount in 4 days . How much material should one begin with so that 4×10 -3kg of the material is left after 6 days

Answer 1

you answer has been attached....

Answer 2

0.256 gm of material should one begin with so that 4×10 -3kg of the material is left after 6 days.

We know, in radioactivity,

When the initial concentration of the radioactive material is N₀ and concentration after n half lives is N, then we can say:

(N/N₀) = (1/2)ⁿ                                                                  ...(1)

Given that, the radioactive material is reduced to 1/16 of its original amount.

So, when N₀ = 1, N = 1/16

(N/N₀) = (1/16) = (1/2)⁴

Comparing it with (1), we get n = 4.

So, 4 half-lives are involved.

Also this process happens in 4 days.

Or in other words, 4 half lives corresponds to 4 days,

1 half life = (4/4) days = 1 day

So, half life of the material is 1 day.

Similarly, no. of half lives in 6 days = 6 = n.

In the second half of the question, we get to know that, N = 4 × 10⁻³ kg.

To find N₀, we take the help of eqn. (1).

So, ( 4 × 10⁻³ / N₀) = (1/2)⁶ = 1/64

⇒  N₀ = (64 ×  4 × 10⁻³) kg = 256× 10⁻³ kg = 0.256kg.

Initial concentration was 0.256kg.