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At an instant, the wave function for an electron is w = f (r,0)e" %u2. Determine the
average value of z-component of magnetic moment for the electron.
(а) — Д в
(b) 243
(c) H3
(d) 3µ3

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Advanced physics, Electromagnetic theory
The quantum-mechanical treatment of the hydrogen atom gives an expression for the wave function ψ, , of the 1s orbital:where ris the distance from the nucleus and a₀ is 52.92 pm. The electron probability density is the probability of finding the elec-tron in a tiny volume at distance rfrom the nucleus and is pro-portional to ψ² . The radial probability distribution is the total probability of finding the electron at all points at distance rfromthe nucleus and is proportional to 4πr² ψ² . Calculate the values(to three significant figures) of ψ, ψ² , and 4πr2² ψ² to fill in the fol-lowing table, and sketch plots of these quantities versus r.
(a) For the 1s wave function, calculate the probability for the electron to be found within the nucleus, considered to be a sphere of radius R. (b) Evaluate the probability for a nucleus of lead (R = 7.1 fm). (c) Suppose instead that a muon (m = 207m) were in its 1s state. What is the probability to find it inside the lead nucleus?
The magnetic dipole moment of a deuterium nucleus is about 0.0005 Bohr magneton. What does this imply about the pres- ence of an electron in the nucleus, as the proton-electron model requires?
Plz complete solution otherwise skip.