
A sample of a radioactive isotope contains
nuclei of the isotope at time
. At time (
), the sample contains (
) nuclei of the isotope. The time interval
is short. Use the symbols
,
,
and
to give expressions for:
the average activity of the sample during the time
,
the probability of decay of a nucleus in the time
,
the decay constant
of the isotope.
The isotope polonium-208 (
) is radioactive and decays to form lead-204 (
). The nuclear equation for this decay is

Data for nuclear masses are given in the table below.
Determine, for the decay of one nucleus of polonium-208:
the change, in
, of the mass
the total energy, in
, released.
The polonium-208 nucleus is initially stationary. The initial kinetic energy of the
nucleus (
-particle) is found to be less than the energy calculated in (i) part 2. Suggest two possible reasons for this difference.