Question:

An atom has an electron in the 3s orbital. Determine the following:

a) The principal quantum number (n) b) The azimuthal quantum number (l) c) The magnetic quantum number (ml) d) The spin quantum number (ms)

Answer:

a) The principal quantum number (n) represents the energy level of the electron. It can be determined by looking at the number in the orbital designation. In this case, the electron is in the 3s orbital, so the principal quantum number is n = 3.

b) The azimuthal quantum number (l) determines the shape of the orbital and ranges from 0 to (n - 1). The s orbital has l = 0, p orbital has l = 1, d orbital has l = 2, and f orbital has l = 3. Since the electron is in the 3s orbital, the azimuthal quantum number is l = 0.

c) The magnetic quantum number (ml) specifies the orientation of the orbital and can range from -l to +l. For the 3s orbital with l = 0, there is only one possible orientation, so the magnetic quantum number is ml = 0.

d) The spin quantum number (ms) determines the direction of electron spin. It can have two possible values: +1/2 and -1/2. Each electron within an orbital must have opposite spin quantum numbers. So, the spin quantum number here can be either ms = +1/2 or ms = -1/2.

In conclusion, for an electron in the 3s orbital, the quantum numbers are:

a) n = 3 b) l = 0 c) ml = 0 d) ms = +1/2 or ms = -1/2