What is the half-life of a radioactive isotope if, on average, 300 out of 320 atoms decay in 6 hours?
February 10, 2021 | education
| 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.
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