Introduction to SAT II Physics

Since there are two nucleons in a deuteron, the binding energy for the deuteron as a
whole is MeV. That energy, converted into mass, is:

The mass of a free proton plus a free neutron is 1.0073 + 1.0086 = 2.0159 amu. The mass
of the deuteron will be 0.0024 amu less than this amount, since that is the amount of
mass converted into energy that binds the proton and the neutron together. So the
deuteron will weigh 2.0159 – 0.0024 = 2.0135 amu.

Decay Rates

On SAT II Physics, you probably won’t be expected to calculate how long it takes a
radioactive nucleus to decay, but you will be expected to know how the rate of decay
works. If we take a sample of a certain radioactive element, we say that its activity, A, is
the number of nuclei that decay per second. Obviously, in a large sample, A will be
greater than in a small sample. However, there is a constant, called the decay constant,
, that holds for a given isotope regardless of the sample size. We can use the decay
constant to calculate, at a given time, t, the number of disintegrations per second, A; the
number of radioactive nuclei, N; or the mass of the radioactive sample, m:

, , and are the values at time t = 0. The mathematical constant e is

approximately 2.718.

The decay constant for uranium-238 is about s–1. After one million years, a 1.00

kg sample of uranium-238 (which has atoms) will contain

Uranium-238 is one of the slower decaying radioactive elements.

Half-Life

We generally measure the radioactivity of a certain element in terms of its half-life,

, the amount of time it takes for half of a given sample to decay. The equation for half-life,
which can be derived from the equations above, is: