Page 440 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 34] ATOMIC PHYSICS 425

Electrons with the same principal quantum number n in an atom are usually about the same distance from
the nucleus and have similar energies. Such electrons are said to occupy the same shell. The higher the value of
n, the greater the energy. Electrons in a given shell that have different orbital quantum numbers l have different
probability density distributions and therefore somewhat different energies; those with the same value of l are
said to occupy the same subshell and have very nearly the same energy. The higher the value of l inagiven
subshell, the greater the energy.

SOLVED PROBLEM 34.12
In the Bohr model of the hydrogen atom, the radius of the electron’s orbit is 5.3 × 10 −11 m in the ground
state. What aspect of the quantum theoretical model might correspond to this relationship?
The maximum probability of finding the electron occurs at this distance from the nucleus.

SOLVED PROBLEM 34.13
How many electrons are able to share an orbital in an atom?
Since an orbital is characterized by a given n,l, and m l , the exclusion principle permits two electrons to occupy
1
1
each orbital in an atom, one with m s =+ and the other with m s =− .
2 2
SOLVED PROBLEM 34.14

What quantum numbers characterize the atomic state in which an electron has the lowest energy?

n = 1 l = 0 m l = 0 m s =± 1
2

SOLVED PROBLEM 34.15
What are the possible values of the orbital and magnetic quantum numbers of an atomic electron whose
principal quantum number is n = 3?
Since l ranges from 0 up to n − 1 for an electron of principal quantum number n and since m l ranges from −l
through 0 to +l for an electron of orbital quantum number l,wehave

l = 0 m l = 0
⎧
⎪m l =+1
⎨
l = 1 m l = 0
⎪
m l =−1
⎩
⎧
⎪ m l =+2
⎪
⎪
⎪ m l =+1
⎪
⎪
⎨
l = 2 m l = 0
⎪
⎪m l =−1
⎪
⎪
⎪
⎪
⎩
m l =−2
SOLVED PROBLEM 34.16
What is the effective nuclear charge that acts on each electron in the outer shell of the chlorine (Z = 17)
atom?
The chlorine atom has closed n = 1 and n = 2 shells with, respectively, two and eight electrons in each. Hence
the n = 3 shell contains seven electrons that are shielded by the 10 inner ones, and the effective charge acting on
these n = 3 electrons is accordingly +7e (Fig. 34-2).