Muonir atoms and the size of the nucleus. The negative muon (symbol pf) is a particle with the same charge as the electron but with a larger mass (m = 207 m,). High-speed muons are produced in violent nuclear collisions. These muons can be slowed down in matter and captured into orbits around the nuclei of atoms in the material. The resulting system. with a negative muon in the inner orbit. is called a muonic atom. After about 2 microseconds (on the average) the muon decays into an electron and two neutrinos. destroying the muonic atom. Despite this brief existence. the muonic atom can be considered stable since its lifetime corresponds to very many periods of revolution of the muon in a Bohr orbit about the nucleus. Because of its large mass relative to the electron. the inner orbit of the muon lies very much closer to the nucleus than that of any electron. This makes it possible to use muonic atoms to probe the size and structure of nuclei.
(a) For a central charge Ze. obtain an expression for the radius r,, of the nth muonic orbit. Express this as a multiple of the radius 0,, of the ﬁrst Bohr (electron) orbit in hydrogen.
(b) For the muonic orbit of (a). what is the energy E, expressed as a multiple of the energy of the lowest state of an electron in the hydrogen atom?
(c) For Z = 13 (aluminum) calculate the energy in keV and the wavelength in Angstroms of the n = 2 —> n = l muonic x-ray transition.
Muonic atoms and the size of the nucleus are determined. The central charge obtained by an expression is provided.
Particle Physics: Nuclear Force, Bohr, & Subatomic Particles
1. Considering Yukawa's hypothesis that the nuclear force should be due to the exchange of massive particles (that he called mesons), calculate the expected mass of this hypothetical meson.
2. Draw a table showing all the elementary spins 1/2 anti-particles arranged in three families horizontally with the individual members of each family vertically. In the table give the names, symbols, electric charges and approximate masses of each anti-particle.
3. In a unit system where c=h=1, the Compton wavelength for an muon is given by ___ (see attachment)___ calculate the numerical value. In the same system, the Bohr radius of a muonic hydrogen atom is given by (see attachment) where alpha is the fine structure constant alpha = 1/137, calculate the numerical value. [A muonic hydrogen atom is just equivalent to a regular hydrogen atom but the electron is substituted by a muon].
4. The weak interaction is assumed to be due to W or Z exchange. If the Z has a mass of 90 GeV/c^2, calculate the range of the weak interactions. How does this compare with the size of a nucleon
? What are the consequences for the likelihood of nuclear beta decay.
5. Two protons are separated by a distance of 10^-15m. Calculate (a) the electric force and (b) the gravitational force on one proton due to the other. Using the relative strengths of the strong, electromagnetic, weak and gravitational forces, estimate (c) the strong force and (d) the weak force between the two protons.
Summarize the four results in order of increasing strength.View Full Posting Details