According to Bohr's model of an atom, which of the following is/are quantized? (a) The total energy of electron is quantized. (b) Angular momentum of electron is quantized. (c) both (a) and (b). (d) None of the above.

#(a)# and #(b)#.

Both energy and angular momentum are observables that correspond to so-called eigenvalues. Eigenvalues are the values that describe a result that occurs consistently, brought about by an observation.

All energies #E# in a quantum mechanical system correspond to eigenvalues that are dependent on a particular quantum number.

An example of atomic energies is the hydrogen atom in the Rydberg equation:

#DeltaE = -"13.6 eV"(1/n_f^2 - 1/n_i^2)#

where:

• #n_i# and #n_f# are the initial and final quantum numbers #n# for the energy levels across which an energy transition occurs.
• #DeltaE# is the energy gap for that transition in units of #"eV"# (#1.602 xx 10^(-19)# #"J"# #=# #"1 eV"#).

#n = 1, 2, 3, . . .# is the principal quantum number, indicating each energy level, corresponding to eigenvalues #E_n#.

Since #n# is quantized, it goes in integer steps, and thus the energy is quantized as well.

The angular momentum of the electron, corresponding to the "shape" of an orbital (not necessarily a thing for Bohr's model, which pretends there are orbits instead), has eigenvalues dependent on the quantum number, #l#:

#l = 0, 1, 2, . . . , n-1# is the angular momentum quantum number, corresponding to the eigenvalue #l(l+1)ℏ^2# of the squared angular momentum, #L^2#.

Clearly, #l# is going in integer steps, so angular momentum is quantized as well.

What about #L_z#, the z-angular momentum, which depends on #m_l#, the magnetic quantum number? Is the z-angular momentum quantized too?