3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a,)3/2 /3ae Zao, where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (b) found? What is the most probable radius (in terms of ao) at which the electron is (c) What is the expectation value of r in this state? Note: f r°e-*dx = 120.

Which of the following sets of quantum numbers n, l, and m¡ would be possible for an excited state of hydrogen? (circle yes or no) I. n= 4, 1= 2, mị II. n= 3, 1=2, m¡ = -2 П. п %3D 2, 1%32, т) %3D+1 IV. п %3D17, 1 %3 2, т %3 —2 =-3 Yes/No Yes/No Yes/No Yes/No

Please answer (i), (v), and (vi). Thank you! (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits a photon and make a transition to the 2s state. What is the frequency v of this photon ? (ii) Now we do not include electron spin angular momentum, and just estimate an effect of a magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum. How many lines of optical transition do we expect ? What is the interval of the frequency in the field B = 0.1 Tesla ? (iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the 3s state, Explain the reason. (iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman) levels. Obtain the level…

Physics 1. Derive the expression ε(ω)=1- ωp 2 / ω2 , ωp2 =ne2 /ε0m for the dielectric constant as a function of ω for a free electron gas of number density n.   2. Show clearly that metals are opaque to light for which ω is less than ωp.   3. Calculate the wavelength cutoff for Na metal if the volume of a primitive unit cell in Na is 35×10-30 m3   how to solve this problem?