Question

Suppose that $\mathbf{4}$ are the limits to the values of an electron in an atom. (a) How many different values of the electrons ${\mathbf{\mu }}_{\mathbf{orb}\mathbf{,}\mathbf{z}}$are possible? (b) What is the greatest magnitude of those possible values? Next, if the atom is in a magnetic field of magnitude $\mathbf{0}\mathbf{.}\mathbf{250}\mathbf{}\mathbf{T}$, in the positive direction of the z-axis, what are (c) the maximum energy and (d) the minimum energy associated with those possible values of${\mathbf{\mu }}_{\mathbf{orb}\mathbf{,}\mathbf{z}}$ ?

Short answer

1. Different possible values of the electrons ${\mathrm{\mu }}_{\mathrm{orb},\mathrm{z}}$ are ${\mathrm{m}}_{\mathrm{l}}=-4,-3,-2,-1,0,+1,+2,+3,+4$.

Step-by-step solution

Listing the given quantities: 

• The limits to the values of ${\mathrm{m}}_{\mathrm{l}}$ for the electron in an atom is ${\mathrm{m}}_{\mathrm{l}}=\pm 4$.

Understanding the concepts of magnetic dipole moment and energy:

In atomic physics, the electron magnetic moment, or more precisely the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge.

(a) Calculations of different possible values of the electron’s  μorb,z: 

The possible values of the electron’s ${\mathrm{\mu }}_{\mathrm{orb},\mathrm{z}}$ in an atom is,

${\mathrm{m}}_{\mathrm{l}}=-4,-3,-2,-1,0,+1,+2,+3,+4$

Hence, there are nine different possible values of the electron’s ${\mathrm{\mu }}_{\mathrm{orb},\mathrm{z}}$.