How do I find the half-life of radioactive isotope?
The half-life of a radioactive isotope is the time taken for half of the atoms in a given sample of the isotope to decay. Radioactivity is random and so, half-life is the average time taken for a large number of atoms.
There are two ways to find the half-life, both come from the decay equation: N = N0e^(-λt) which is an exponential relationship*.
Where N is the number of atoms of the isotope left at time t and N0 is the number of atoms when t =0. λ is known as the decay constant and is the probability that an atom will decay per unit time. If you are given the decay constant you may find the half-life T1/2 by setting N = N0/2 and rearranging to find t = T1/2. Or if you are given N and N0 you may find λ and follow the previous steps.
*Make sure you familiar with exponentials and logs before attempting this topic
Related Physics A Level answers
All answers ▸Why do capacitors dis/charge suddenly and then slow down?
What is an equipotential in an electric/gravitational field?
Newton's Law of Gravitation states: F=GMm/r^2, where G is the gravitational constant (6.67×10−11m^3kg^−1s^−2). Kepler's Third Law, states t^2=kR^3. The mass of the sun is 1.99x10^30kg. Find the value of k and its units
Use the kinetic theory of gases to explain why the pressure inside a container increases when the temperature of the air inside it rises. Assume that the volume of the container remains constant.