|1. a) The electron in the hydrogen atom is subjected to a magnetic field produced by the proton. Explain this phenomenon. (i) Given that the radius of the electron orbit is ľand the electron speed is v, calculate the magnetic field produced by the proton at the location of the electron. Using the Bohr model, derive a formula for the energy level splitting due to the magnetic field calculated in (i) in terms of the quantum number n. Hence, calculate the splitting of the n=2 level in eV. (ii) (iii) b) Consider a particle in a superposition state with the wave function + e Defie yo Y! ii) the wowe dunediong re, fhad the Normalize Constant A. What is the probability that a measurement of Lz will yield a value Lz = 0? in) Find the expectation values of L?
|1. a) The electron in the hydrogen atom is subjected to a magnetic field produced by the proton. Explain this phenomenon. (i) Given that the radius of the electron orbit is ľand the electron speed is v, calculate the magnetic field produced by the proton at the location of the electron. Using the Bohr model, derive a formula for the energy level splitting due to the magnetic field calculated in (i) in terms of the quantum number n. Hence, calculate the splitting of the n=2 level in eV. (ii) (iii) b) Consider a particle in a superposition state with the wave function + e Defie yo Y! ii) the wowe dunediong re, fhad the Normalize Constant A. What is the probability that a measurement of Lz will yield a value Lz = 0? in) Find the expectation values of L?
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part b
Transcribed Image Text:|1. a) The electron in the hydrogen atom is subjected to a magnetic field produced by the
proton. Explain this phenomenon.
(i)
Given that the radius of the electron orbit is ľ and the electron speed is v, calculate
the magnetic field produced by the proton at the location of the electron.
Using the Bohr model, derive a formula for the energy level splitting due to the
(ii)
magnetic field calculated in (i) in terms of the quantum number n.
Hence, calculate the splitting of the n=2 level in eV.
(ii)
b)
Consider a particle in a superposition state with the wave function
Define
yo Y!
Normalize te wowe junedion, re, fhad the
constant A.
What is the probability that a measurement of L, will yield a value Lz = 0?
Find the expectation values of £?.
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