What is the half-life of a radioactive isotope if, on average, 300 out of 320 atoms decay in 6 hours?

Let’s start with a short entry given:

n0 = 320;

n = 300;

t = 6 hours.

To find:

T -?

Let’s apply the law of radioactive decay to the solution:

N = N0 * 2 ^ (- t / T);

Find N as the difference between n0 and n and get:

N = n0 – n = 320 – 300 = 20.

Substitute the known values into the formula and get the equation:

20 = 320 * 2 ^ (- t / T);

We solve the resulting exponential equation:

2 ^ (t / T) = 16;

2 ^ (t / T) = 2 ^ 4;

The bases of the degrees are equal, so we can equate the exponents:

t / T = 4;

Substitute t = 6 into the formula:

6 / T = 4;

T = 1.5 h.

Answer: 1.5 hours.