The Bohr atom, nuclear decay

Bohr atom

Problem:

Consider a Bohr-type, classical model of a hydrogenic atom, where a structureless electron with charge -qe is orbiting a (stationary) structureless nucleus with charge Zqe in a circular orbit in the xy-plane without radiating.  Let the angular momentum vector of the electron be L = Lk and have magnitude L = nħ.
(a)  What is the orbital radius r0 of the electron?
(b)  What is the kinetic energy of the electron and what is its total energy?
(c)  What is the magnetic dipole moment μ of the atom?

Solution:


Nuclei and particles

Problem:

Calculate the binding energy of the deuteron, which consists of a proton and a neutron, given that the mass of a deuteron is 2.013553 u.

Solution:

Problem:

Consider the case of a chain of two radioactive decays. Nucleus A decays into another B by one process, then B decays into another C by a second process, i.e. A → B → C.
The mean life of A is τA = 1/λA, and the mean life of B is τB = 1/λB,
Initially N0A nuclei of type A are present and N0B = 0.
(a)  Find the decay rate (the number of decays per second) for B in terms of  N0A, λA, and λB,
(b)  Find approximate expressions for the decay rate if
(i)  λA >> λB,  (ii)  λA << λB,  (iii)  λA ≈ λB,

Solution: