Culver City H.S. • AP ChemistryName

7 • Atomic Structure & PeriodicityPeriod Date

NOTES- EM WAVES & ATOMIC ORBITALSs

Light

A wave describes the oscillations by which energy travels in space and can be characterized by three properties:

  • Wavelength ()the length of one oscillation (cycle) Unit: m
  • Frequency ()the number of oscillations (cycles) the wave makes each secondUnit: s‒1 or Hertz (Hz)
  • Speedthe distance a wave travels per unit timeUnit: m/s

Electromagnetic radiation, or light, can be described as a wave because it has wave properties. While there are many forms of light with different wavelengths and frequencies, they all travel at the same speed, the speed of light, c. Notice that the wavelength and frequency are inversely related.

c =  ·  = 2.9979 × 108 m/s

The energy of light is directly related to its frequency (and inversely related to its wavelength):

E = h ·  =

where h, Planck’s constant, is 6.626 × 10‒34 J·s, and the energy, E, is in Joules.

Example 1: Find the frequency and energy of light corresponding to the following wavelengths: 410.2 nm, 434.1 nm, 486.1 nm, and 656.3 nm. (1 nm = 10‒9 m)

Electron Energy Levels

In 1911, Ernest Rutherford proposed the Nuclear Model of the Atom: an atom is mainly empty space with a tiny, dense nucleus of positively-charged protons and with negatively-charged electrons orbiting the nucleus.

When white light shines through a prism, light of different wavelengths bend at different angles, and a continuous spectrum is observed. However, when a sample of hydrogen was excited with electricity, light at specific wavelengths of light were observed: 410.2 nm (violet), 434.1 nm (violet), 486.1 nm (blue), and 656.3 nm (red).

In 1913, Niels Bohr, a Danish physicist, proposed that the electrons orbited the nucleus at specific, discrete energy levels (n = 1, 2, 3, …). We say that these energy levels are quantized.

As electrons are excited, they jump to higher energy levels. When these electrons relax to lower energy levels, they emit light with the energy corresponding to the difference between the energy levels.

He suggested that each energy level can only hold a certain number of electrons, so when an energy level is filled up, electrons then occupy the next level. These are called principal energy levels.

In general the higher the principal energy level, the further away the electron is from the nucleus.

Atomic Orbitals

In 1925, Werner Heisenberg, a German physicist, proposed the Uncertainty Principle: the exact position and speed of an electron cannot be known. In other words, electrons don’t follow circular orbits, but can actually be anywhere. The electron’s location can be thought of as an electron cloud.

In 1926, Austrian physicist Erwin Schrödinger, using mathematical models, stated that instead of electrons having orbits, there are regions of space where electrons are likely to be found, called atomic orbitals. He also found different types of atomic orbitals, called sub-levels, are available in each electron shell.

  • s-sublevels contains only one spherical-shaped s orbital.
  • p-sublevels contain three different dumbbell-shaped p-orbitals with the same energy, pointing along the x-, y-, and z-axes.
  • d-sublevels contain five different d-orbitals (whose shapes are complicated) with the same energy.
  • f-sublevels contain seven different f-orbitals (whose shapes are complicated) with the same energy.

The higher the principal energy level, the more sub-levels it contains.

  • First PrincipalEnergy Level (n = 1) ‒ contains only one s-sublevel, which we will call the 1s sublevel. There is only one orbital in the 1s sublevel.
  • Second Principal Energy Level (n = 2) ‒ contains two sublevels: an s-sublevel (2s) and a p-sublevel (2p). There is one orbital in the 2s sublevel and three orbitals in the 2p sublevel.
  • Third Principal Energy Level (n = 3) ‒ contains three sublevels: an s-sublevel (3s), a p-sublevel (3p), and a d-sublevel (3d). There is one orbital in the 3s sublevel, three orbitals in the 3p sublevel, and five orbitals in the 3d sublevel.
  • Fourth Principal Energy Level (n = 4) ‒ contains four sublevels: an s-sublevel (4s), a p-sublevel (4p), a d-sublevel (4d), and an f-sublevel (4f). There is one orbital in the 4s sublevel, three orbitals in the 4p sublevel, five orbitals in the 4d sublevel, and seven orbitals in the 4f sublevel.

We can continue past the fourth principal energy level. In general, on the nth electron shell, there are nsublevels with a total of n2orbitals.

Energies of Atomic Orbitals

In general, orbitals on lower principal energy levels have lower energies. However, in an atom with more than one electron, there can be some unexpected shifts in energy of sublevels.Every orbital can be occupied by a maximum of two electrons.

Principal Energy Level / Sublevel / Orbitals in that Sublevel / Total Orbitals in the Sublevel
n = 1 / 1s / 1 / 1
n = 2 / 2s / 1 / 4
2p / 3
n = 3 / 3s / 1 / 9
3p / 3
3d / 5
n = 4 / 4s / 1 / 16
4p / 3
4d / 5
4f / 7

Example 2:

  • How many total orbitals are in the n = 6 principal energy level? How many electrons can fill the n = 6 principal energy level?
  • How many orbitals are in the 5d sublevel? How many electrons can fill the 5d sublevel?
  • How many sublevels are in the n = 5 principal energy level?
  • Arrange these sublevels in increasing energy: 3s 3p, 3d, 4s, 4p

Problem Sets

Set 1.
(a) / The laser in a CD player uses light with a wavelength of 7.80 × 102 nm. Calculate the frequency of this light.
(b) / Microwave radiation has a wavelength on the order of 1.0 cm. Calculate the frequency and the energy of a single photon of this radiation.
(c) / A photon of UV light possesses enough energy to mutate a stand of human DNA. What is the energy of a single UV photon having a wavelength of 25 nm?
(d) / It takes 7.21 × 10–19 J of energy to remove an electron from an iron atom. What is the maximum wavelength of light that can do this?
Set 2.
(a) / Which electron is, on average, close to the nucleus: an electron in a 2s orbital or an electron in a 3s orbital?
(b) / Which electron is, on average, further from the nucleus: an electron in a 3p orbital or an electron in a 4p orbital?
(c) / Which of these orbitals do not exist?
1s1p7d9s3f4f2d
(d) / How many orbitals are in the n = 5 electron shell? How many electrons can fill the n = 5 electron shell?
(e) / How many electrons can fill the 5f subshell?
(f) / How many subshells are in the n = 7 electron shell? How many orbitals are in the n = 7 electron shell?

Answers

Set 1.

(a) = = = 3.8 × 1014 Hz

(b) = = = 3.0 × 1010 Hz
E = = = 2.0 × 10‒23 J

(c)E = = = 8.0 × 10‒18 J

(d) = = = 2.8 × 10‒7 m

Set 2.

(a)2s, because it’s in a lower shell.

(b)4p, because it’s in a higher shell.

(c)1p, 3f, 2d

(d)5s + 5p + 5d + 5g + 5h = 1 + 3 + 5 + 7 + 9 = 25 orbitals

25 orbitals × 2 e‒/orbital = 50 electrons

(e)5f = 7 orbitals × 2 e‒/orbital = 14 electrons

(f)7 subshells

1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 orbitals