Question

How to set up the formula to figure the half-life of radioactive material.

Example: 100 g of nitrogen-16 decays to 12.5 g of nitrogen-16 in 26.5 seconds. How do we plug in the info we have into the formula?

Answer 1

The formula to calculate the half-life of a radioactive material is t1/2 = (ln2 / k), where t1/2 is the half-life, ln is the natural logarithm, and k is the decay constant. To calculate the half-life, you need to know the initial mass of the material and the mass remaining after a certain period of time. In the given example, the half-life is 26.5 seconds.

Step-by-step explanation:

The formula to calculate the half-life of a radioactive material is:

t1/2 = (ln2 / k)

Where:
- t1/2 is the half-life of the material
- ln is the natural logarithm
- k is the decay constant

To calculate the half-life, you need to know the initial mass of the material and the mass remaining after a certain period of time. In the given example, the initial mass is 100 g and the remaining mass after 26.5 seconds is 12.5 g. Substituting these values into the formula:

t1/2 = (ln2 / k)
26.5s = (ln2 / k)

To solve for k, we need to rearrange the formula:

k = ln2 / t1/2

Substituting the values:

k = ln2 / 26.5s

To find the half-life:

t1/2 = ln2 / k
t1/2 = ln2 / (ln2 / 26.5s)
t1/2 = 26.5s