Questions from Modern Physics

Q: Show that Φ(ϕ)= eimlϕ = Φ(ϕ +

Show that Φ(ϕ)= eimlϕ = Φ(ϕ + 2π) (that is, show that Φ(ϕ) is periodic with period 2π) if and only if ml is restricted to the values 0, ±1, ±2,……. (Hint: Euler’s formula states that eif = cos ϕ + i si...

Q: A hydrogen atom is in a d state. In the absence

A hydrogen atom is in a d state. In the absence of an external magnetic field, the states with different ml values have (approximately) the same energy. Consider the interaction of the magnetic field...

Q: A hydrogen atom in a 3p state is placed in a uniform

A hydrogen atom in a 3p state is placed in a uniform external magnetic field B. Consider the interaction of the magnetic field with the atom’s orbital magnetic dipole moment. a. What field magnitude...

Q: In Fig. 40.28, how does the probability of

In Fig. 40.28, how does the probability of finding a particle in the center half of the region -A From Fig. 40.28:

Q: Model a hydrogen atom as an electron in a cubical box

Model a hydrogen atom as an electron in a cubical box with side length L. Set the value of L so that the volume of the box equals the volume of a sphere of radius a = 5.29 * 10-11 m, the Bohr radius....

Q: A hydrogen atom undergoes a transition from a 2p state to the

A hydrogen atom undergoes a transition from a 2p state to the 1s ground state. In the absence of a magnetic field, the energy of the photon emitted is 122 nm. The atom is then placed in a strong magne...

Q: A hydrogen atom in the 5g state is placed in a magnetic

A hydrogen atom in the 5g state is placed in a magnetic field of 0.600 T that is in the z-direction. a. Into how many levels is this state split by the interaction of the atom’s orbital magnetic dipo...

Q: A hydrogen atom in the n = 1, ms = -

A hydrogen atom in the n = 1, ms = - 1/2 state is placed in a magnetic field with a magnitude of 1.60 T in the +z- direction. a. Find the magnetic interaction energy (in electron volts) of the electr...

Q: a. If you treat an electron as a classical spherical object

a. If you treat an electron as a classical spherical object with a radius of 1.0 * 10-17 m, what angular speed is necessary to produce a spin angular momentum of magnitude 3/4 ħ? b. Use v = rω and...

Q: The hyperfine interaction in a hydrogen atom between the magnetic dipole moment

The hyperfine interaction in a hydrogen atom between the magnetic dipole moment of the proton and the spin magnetic dipole moment of the electron splits the ground level into two levels separated by 5...