Question

a radioactive sample has a half life of 5.0 mins. what fraction of the sample is left after 20 mins.

Answer 1

Answer:

The general formula for this problem is:

%left = (1/2)^(time past / half-life)

In this case, %left = (1/2)^(20/5) = 0.5^4 = 0.0625 = 1/16

Consider 18 minutes:

%left = (1/2)^(18/5) = 0.5^3.6 = 0.0825

Explanation:

Answer 2

Given,

Time period of half life=5mins

To Find,

Fraction of the sample is left after 20 mins.

Solution,

Lets, take initially amount of the substances was x mole.

Half life time is 5  mins as it it mentioned.

Means ,20/5=4

So ,mainly it is going to ask about the fraction left after the 4 life times.

Since ,the reaction is first order we can use the general formula for concentration left after n half life time is  ,

(1/2)^n× A, where A is initial concentration.

So ,A'=(1/2)^4×A

        =A/16

A'=A/16

Means, fraction left 1/16.

Hence, 1/16 of the sample is left after 20 mins.