1. Nuclear Physics 5 Exponential Decay Friday, 16 November 2018
Leeds City College

2. Exponential Decay
The fraction of atoms decaying at any given time is constant. In this diagram, we see that after t1 seconds, 80 % of the atoms are left. After t2 seconds 0.8 × 0.8 = 64 % are left.
The half life is the time taken for 50 % of the atoms to decay. After 2 half lives, 25 % remain.
Friday, 16 November 2018
Leeds City College

3. Decay Constant
The decay constant is the proportion of the sample that are likely to decay in unit time.
It is described by the equation:
The minus sign shows that the number of atoms left is going down.
The change in number per unit time can be measured as the activity:
Friday, 16 November 2018
Leeds City College

4. Exponential Decay Equation
For longer periods of time, a different but related equation is used. It is derived from the previous equation by calculus. You are not required to know this derivation.
N – number of atoms remaining;
N0 – original number of atoms.
e – the exponential number = 2.718…
l – the decay constant (s-1);
t – time (s)
Friday, 16 November 2018
Leeds City College

5. Half Life
Half life is the time taken for half the remaining atoms to decay.
Rearrange
Rearranging:
Minus signs cancel out
Which gives:
This can be written as:
Take natural logarithms:
Friday, 16 November 2018
Leeds City College