505
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121 â 10 = 11.
2Because the strong nuclear force keeps them bound.
322 in both cases.
4Beta minus decay.
5One alpha decay and two beta minus decays.
6No. After another half-life, half of what was there before will decay.
725 Ã 1025 nuclei of the radioactive isotope are left so 2 half-lives went by.
8It is still 0.5, the decays are random.
9aDeviations from Rutherford scattering. The deviations imply that a new force is acting on the alpha particles as they get too close to the nuclear surface.
bThe approximate constancy of the binding energy per nucleon for larger nuclei. For large nuclei, any one nucleon is surrounded by the same number of nucleons, thus the same energy would be required to remove that nucleon from the nucleus.
10Nuclear energy levels differ in energy by MeV and atomic energy levels by eV. So the photons in nuclear transitions have wavelengths that are of order 106 smaller than those in atomic transitions.
11It is not 6! Express the decay constant as Î» = 6 hourâ1 = 0.1 minâ1. The probability of decay within 1 min is 0.1. The probability of no decay within 1 min is then 0.9. The probability of no decay in 60 min is then 0.960 and so the probability of decay in 1 hour is 1 â 0.960 = 0.998. Similarly, Î» = 6 hourâ1 = 0.1 minâ1 = 1.667 Ã 10â3 sâ1. What is the probability of a decay in 1 min? We expect the answer to be 0.1. Indeed: probability of no decay within 1 s = 1 â 1.667 Ã 10â3 = 0.9983. Probability of no decay in 60 s = 0.998360. So probability of decay in 60 s is 1 â 0.998360, which is about 0.1 as expected.