Question

Suppose 128 ounces of a radioactive substance exponentially decays to 28 ounces in 6 hours. What is the half-life of the substance? The half-life is:

Answer 1

Answer:

The half life of the substance that decays from 128 to 28 in 6 hours is 2.736 hours.

Explanation:

Step 1 : Write down the formula for getting the remaining amount of a radioactive substance.

Let Ao be the initial amount, t be the time taken to decay and t½ the half life. The amount at time t A(t) is given by :

A(t) = Ao(½)^t/(t½)

Step 2 : Identify the values given in the question.

A(t) = 28

t = 6

Ao = 128

t½ =?

Step 3 : Substitute the values to get the half life.

We have:

28 = 128(½)^6/t½

28/128 = (½)^6/t½

0.21875 = (½)^6/t½

Taking ln on both sides we have :

ln 0.21875 = 6/t½ ln (½)

-1.5198 = (6 × - 0.6931) / t½

-1.5198 t½ = - 4.1586

t½ = 2.736 hours.

Answer 2

Answer:The half life of the substance that decays from 128 to 28 in 6 hours is 2.736 hours