8.1.4

Test yourself

When an object is radioactive it releases radioactive particles but as time passes the rate of particles decreases. This is called decay.

### Random decay

• The decay of a radioactive substance is random and spontaneous.
• To measure decay, we must look at the count rate over a long time to see if it decreases.

### Probability

• The probability that a given nucleus will decay in a given time is proportional to the number of nuclei. The equation for calculating the rate of decay is:
• The rate of decay of nuclei = decay constant x the number of nuclei
• $\frac{{\Delta}N}{{\Delta}t}=-{\lambda}N$
• ${\lambda}$ is the decay constant.
• $N$ is the number of nuclei.

## The Exponential Law

The reduction in the rate of decay decreases according to an exponential pattern.

### Exponential decay

• From the equation for the rate of decay, we can find an exponential relationship between the number of nuclei and time.
• The equation for the rate of decay of nuclei is:
• $\frac{{\Delta}N}{{\Delta}t}=-{\lambda}N$
• The exponential relationship corresponding to this is:
• $N={N_0}e^{-{\lambda}t}$
• ${N_0}$ is the initial number of nuclei.

### Activity

• The activity of a sample can be found by using the decay constant and the number of nuclei. The equation for activity is:
• Activity = decay constant x number of nuclei
• $A={\lambda}N$
• The exponential relationship corresponding to the activity is:
• $A={A_0}e^{-{\lambda}t}$