Chapter 5 Electrons in Atoms

Chapter 5 Electrons in Atoms Wave Nature of Light

A form of energy, electromagnetic radiation exhibits wavelike properties. Visible light is an example of electromagnetic radiation. A wave has certain characteristics.

Wavelength = distance between crests or troughs, symbol λ Amplitude = height of wave

Frequency, ν = number of waves that pass a given point per second. The units of waves per second are hertz (Hz) - SI units. Frequency is usually expressed in

“waves per second” or 1/s or s

e.g. 300 Hz = 300 waves per second = 300 s-1 (note the word cycle or wave is omitted) or 300 cycles per second

All electromagnetic waves travel at a speed of light, which is 3.00 x 10

m/s, given the symbol c.

Useful formula c = λ ν

speed of = wavelength * frequency light

Electromagnetic spectrum p.120

Practice problems 1-4, page 121, page 147 #68, 67

Electromagnetic Spectrum (cont)

Which types of waves or rays have the highest energy?

If the wavelength of microwave radiation is 3 x 10

m, will the frequency of this radiation be in the high or low end of the range in the electromagnetic spectrum?

Therefore, we can say that

  1 wavelength is inversely proportional to frequency

 Particle Nature of Light

Failings of the wave model of light – does not explain why:- 1) Heated objects emit light of certain frequencies only.

2) When colored light of a specific frequency shines on some metals then electrons are emitted. This is known as the photoelectric effect, which can be used in calculators. Here the incident light is converted by photoelectric cells to electrical energy.

Einstein proposed that electromagnetic radiation exhibits both wave and particle

properties. Light can exist as waves or a stream of tiny particles called photons. Photons can be thought of as packets of energy; so one photon carries a quantum of energy.

Einstein proposed the following relationship between energy and frequency.

E

= h h= 6.626 x 10

J.s, Planck’s constant.

p 124 Practice problem 5 and 6.

Atomic Emission Spectra

When atoms are excited by for example heat or electricity, then the atoms absorb energy, which is later emitted as light. If this light is then passed through a prism, it is split up into light of different frequencies and produces an

– which is a series of individual lines. Each element has its own atomic emission spectrum.

Balmer Series of spectral lines (visible) transition to the n=2 level

An H electron is normally located in the ground state in the n=1 level. When excited the electron can drop from higher energy levels to a lower energy level (n=2 in diagram).

When electrons do this, energy is emitted in the form of light. Each transition or drop has a certain energy associated with it and produces light of a certain frequency from E=h.

When electrons drop back to the n=1 level then E and  are high and light emitted is in the ultra violet region of the spectrum (lines known as the Lyman series). Transitions down the n=3 level give spectral lines in the infrared region (Paschen series).

Hydrogen’s Atomic Emission Spectrum

Bohr Model of the Atom

Bohr believed that electrons traveled in circular orbits around the nucleus. The hydrogen atomic emission spectra is composed of discrete lines that correspond to a certain

frequency of light emitted. The Bohr model correctly predicted the frequencies of the spectral lines for hydrogen but failed to explain the spectrum of other elements.

The Quantum Mechanical Model of the Atom.

Electrons as waves

Loius de Broglie (1892-1987) predicted that all moving particles have wave

characteristics. He derived an equation for the wavelength () of a particle of mass (m) moving at velocity (v).

= h h= Planck’s constant.

mv

The Heisenberg Uncertainty Principle:

states that it is impossible to know the exact position and velocity of an electron.

Schrődinger studied the wave properties of an electron. Electrons are located in atomic orbitals, which surround the nucleus of the atom. The Quantum Mechanical Model assigns quantum numbers to the atomic orbitals:-

The principal quantum number, n, describes the relative size and energy of atomic

orbitals – so the principal quantum number describes the energy level and distance from

the nucleus – n can have values 1, 2, 3 … n.

Electronic Arrangement and Quantum Numbers

The electrons fill up the energy levels starting at the lowest energy level. The formula for finding the maximum number of electrons in a particular energy level is 2n

, where n = no. of the energy level.

No. of Energy Level Maximum no.of e

s.

Pauli Exclusion Principle

This states that no two electrons in any atom have the same amount of energy associated with it and therefore cannot follow the same path.

Therefore considering the first energy level, n= 1 ( n is the first quantum number),

contains 2 electrons (maximum) these electrons have different spins :- one clockwise and one anti-clockwise. Different spins have different amounts of energy associated with them and therefore follow a different path. We denote this as ↑↓.

In each energy level, there can be several sub-levels, 2

quantum number, l, with levels s, p, d, f. The s level can take a maximum of two electrons, the p level – 6 electrons, the d level - 10 electrons and the f energy level -14 electrons.

The letter describing the sub-level is preceded by the value of n for the energy level e.g.

3d, 4f, 2p.

Each sublevel contains orbitals (space occupied by a pair of electrons). The third

quantum number, m

(magnetic quantum number) is used to describe each orbital within in a sublevel. There are 3 orbitals for the p sublevel, 5 orbitals for the d sublevel, and 7 orbitals for the f sublevel.

Finally, the fourth quantum number m

describes direction of electron spin :- clockwise or anticlockwise.

Note: No two electrons in an atom can have the same set of quantum numbers.

Relative Stability of Electron Configurations General Rule:

Atoms with full outer levels are particularly stable. (that is less reactive)

Usually the outer level is full when it contains 8 electrons (exception He: the outer level is full with 2 electrons).

Note: the helium atom has a full outer level of 2 electrons and He is very unreactive and stable.

The 8 electrons are made up of 2 electrons in the outer s sublevel and 6 in the outer p sublevel. These 8 outer level electrons are responsible for the lack of reactivity of the atom. This is known as the octet rule.

Other Stable Configurations:

An atom with a half filled or completely filled sublevels are also stable.

Example: Cr (Z=24) has a configuration of [Ar] 4s

3d

. Here the d orbital is half filled.

And, Cu (Z=29) has a configuration of [Ar]4s

3d

. Here the d orbital is completely filled.

Note, we would have expected a configuration of [Ar]4s

3d

, but this is less stable.

Order of Stability:

Full outer level > Full sublevel > Half full sublevel > No special arrangement Properties of Metals and Non-Metals

Metals Non Metals

Hard, shiny solids Gases or brittle solids If solid, surfaces are dull

Conductors of heat and electricity Insulators, non-conductors of heat and electricity

Usually high melting and boiling points Usually low melting and boiling points Have 3 or fewer electrons in the outer

level

Have 5 or more electrons in the outer level

On left hand side of Periodic Table – most elements are metals

On right hand side of Periodic Table

Metalloids have properties of metals and non-metals e.g. B - boron, Si – silicon, Ge –

germanium, Sb – antimony, Te – tellurium,, Po – polonium, and At - astatine