An atom in a 3d state emits a photon of wavelength 475.082 nm when it decays to a 2p state. Find the allowed transitions if the atom is now in an external magnetic field of 3.500 T. Ignore the effects of the electron’s spin.

Given an electron in the n=4 state of a hydrogen atom. What values would you get for m_l (Azimuthal part: magnetic quantum number) when l = 0,1,2,3.

For the hydrogen atom in the 4d excited state find the possible values of n,l,m,m,, and mj. Give the term notation for each possible configuration.

3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.