Chapter 5 Electrons in Atoms

5.1 MODELS OF THE ATOM:

1803 – John Dalton – tiny indestructible particles with no internal structure

1897 – J.J. Thomson – electrons are embedded in a sphere of positive electrical charge – the “plum pudding model”

1904 – Hantaro Nagaoka – suggests that the atom has a central nucleus, electrons move like like the rings of Saturn

1911 – Ernest Rutherford – atoms have a small dense positive nucleus and electrons move around the nucleus

1913 – Niels Bohr – the electron moves in fixed circular orbits at fixed distances from the nucleus

1923 – Louis de Broglie – Moving particles like electrons have some properties of waves

1926 – Erwin Schrodinger – develops a mathematical equation to describe the motion of electrons in an atom leading to the electron cloud model

1932 – James Chadwick – confirms the existence of neutrons, which have no charge, the nucleus contains neutrons and positively charged protons

Energy Levels – represents the fixed energy levels that an electron can exist, electrons can move up or down in energy levels if they gain or lose energy.

Quantum – is the amount of energy required to move an electron from one energy level to another energy level. The energy of an atom is said to be quantized and the energy lost or gained by an electron is not always the same. The energy levels are like rungs on a ladder that are spaced closest at the top of the ladder. Electrons can change levels, it requires less energy to switch levels the farther the electron is from the nucleus.

The Quantum Mechanical Model: is the modern description of the electrons in atoms derived from mathematical equations by Erwin Schrodinger.

The quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus.

Atomic Orbitals: is thought of as a region of space in which there is a high probability of finding an electron

The energy levels of electrons in the quantum mechanical model are labeled by principle quantum numbers (n) where n = 1,2,3,4,5,6,7

For each principle energy level there may be several orbitals with different energy levels

These energy levels within a principle energy level are called sublevels

Each sublevel contains a certain number of orbits

n = 1 has 1 sublevel 1s one orbitn = 2 has 2 sublevels 2s one orbit, 2p three orbitalsn = 3 has 3 sublevels 3s one orbit, 3p three orbitals, 3d five orbitalsn = 4 has 4 sublevels 4s one orbit, 4p three orbitals, 4d five orbitals, 4f seven orbitals

Each electron has a set of four numbers, called quantum numbers, that specify it completely; no two electrons in the same atom can have the same four.

1. The "primary quantum number," which is given the symbol n, corresponds to the rows you see on the periodic chart 2. The second quantum number is known as l, the angular quantum number refers to sublevel. A value of l=0 corresponds to s, l=1 is p, l=2 is d, and so forth. 3. The magnetic quantum number (m) can be any integer between -l and +l. If l = 2, m can be either -2, -1, 0, +1, or +2

Each electron has a set of four numbers, called quantum numbers, that specify it completely; no two electrons in the same atom can have the same four.

The principal quantum number, n •determines the size of an orbital (bigger n = bigger orbitals) •largely determines the energy of the orbital (bigger n = higher energy) •can take on integer values n = 1, 2, 3, ...,   •all electrons in an atom with the same value of n are said to belong to the same shell •spectroscopists use the following names for shells

The azimuthal quantum number,

•designates the overall shape of the orbital within a shell •affects orbital energies (bigger = higher energy) •all electrons in an atom with the same value of are said to belong to the same subshell •only integer values between 0 and n-1 are allowed •sometimes called the orbital angular momentum quantum number •spectroscopists use the following notation for subshells

 subshell name

0 s

1 p

2 d

3 f

The magnetic quantum number m - Determines the orientation of orbitals within a sublevel - Does not affect orbital energy - Only intergers between –l and +l are allowed - The number of m values in a sublevel is the number of orbitals in the sublevel

L values of m orbitalsL values of m orbitals

00 00 11

11 1, 0, -11, 0, -1 33

22 2,1,0,-1,-22,1,0,-1,-2 55

33 3,2,1,0,-1,-2,-33,2,1,0,-1,-2,-3 77

The spin quantum number, s -several experimental observations can be explained by

treating the electron as though it were spinning

-spin makes the electron behave like a tiny magnet

-spin can be clockwise or counterclockwise

- spin quantum number can have values of +1/2 or -1/2

http://antoine.frostburg.edu/chem/senese/101/electrons/

The maximum number of electrons per energy level

1 – 22 – 83 – 184 - 32

5.2 ELECTRON ARRANGEMENT IN ATOMS:

Electron configuration – is the way that electrons are arranged into various orbitals around the nuclei of atoms.

Three rules exist in electron configuration1. Aufbau Principle2. Pauli Exclusion Principle3. Hund’s Rule

Aufbau’s Principle: electrons occupy the orbitals of lowest energy first. Within a principle energy level, the s sublevel is always the lowest-energy sublevel. However, the range of energy levels within a principal energy level can overlap the energy levels of another principle level

Pauli’s Exclusion Principle: an orbital may describe at most two electron. To occupy the same orbital, two electrons must have opposite spin – the electrons spins are then paired. Spin is a quantum mechanical property of electrons and may be thought of a clockwise or counterclockwise.

One electron enters each orbital until all orbitals contain one electron with the same spin direction

Each electron has a set of four numbers, called quantum numbers, that specify it completely; no two electrons in the same atom can have the same four.

Hund’s Law: states that electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible. Electrons then occupy each orbital so that their spins are paired with the first electron in the orbital eventually each orbital can have two electrons with paired spins

Exceptional Electron Configuration: Some actual electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels, but they are more stable than other configurations. This overcomes the small differences between the energies of the 3d and 4s sublevels.

Exceptions to the aufbau principle are due to subtle electron – electron interactions in orbitals with very similar energies

There are some exceptions to the to the aufbau principle.  The first is chromium (Z = 24), the aufbau principle predicts the an electron configuration of  [Ar]3d44s2 but experimentally we find it to be  [Ar]3d54s1.  The next exception found is that of copper (Z = 29), the predicted electron configuration is  [Ar]3d94s2 but experimentally we find it to be  [Ar]3d104s1.  The reason for these and other exceptions are not completely understood, but it seems that a half-filled 3d subshell in the case of chromium or a completely-filled  3d subshell in the case of copper lend a special stabilty to the observed electron configurations.  There is no need to dwell on these exceptions, the point to remember is that the aufbau principle predicts the correct electron configuration most of the time and that the energy of the predicted electron configuration is very close to the ground state energy.

5.3 PHYSICS AND THE QUANTUM MECHANICAL MODEL:

LIGHT:

What led Shrodinger to his equations? The answer is Light!

The quantum mechanical model grew out of the study of light by Newton, who tried to describe the behavior of light as a particle and could behave like a wave.

A wave is made of distinct parts that can be measured, studied and compared.

Amplitude – height of wave from resting positionCrest – Highest part of the waveTrough – Lowest part of the waveWavelength – distance between crests or troughs is the symbolFrequency – number of wave cycles per unit time – unit – Hertz - cycle per second f = 1/TPeriod – Time for one wave cycle measured in seconds T = 1/f

The wavelength and the frequency are inversely proportional to each other

The relationship between frequency and wavelengthThe mathematical relationship is:

According to the wave model, light consists of electromagnetic waves.Electromagnetic radiation includes the following;

Notice how the wavelength, frequency, and energy of the wave changes. All electromagnetic waves travel in a vacuum at a speed of 2.998 x 108 m/s

Sunlight consists of light with a continuous range of wavelength and frequencies

When sunlight passes through a prism, the different wavelengths separate into different frequencies forming a spectrum of colors.

Atomic Spectra:When atoms absorb energy, electrons move into higher energy levels, when the electrons lose energy they return to the lower level and give off the excess energy in the form of light. Each atom express its own individual light signature called an atomic emission spectrum

As light from an element is passed through a spectrum the frequencies of light are separated into separate distinct lines

An Explanation of Atomic Spectra:

Ground state- the lowest possible energy level of an electron

Excited state – the level to which an electron is moved when it gains energy

A quantum of energy in the form of light is emitted when the electron drops back to its ground state

Because the emission of light occurs in one abrupt step, Bohr knew that the quantum energy of light produced by the electron was directly proportional to the product of Plank’s constant and the frequency of the emitted light.

Therefore each transition produces a line of a specific frequency in the spectrum

The three groups of lines produced by the Hydrogen spectrum is seen below

There are 3 series of lines producedas the electrons transition from Excited states to ground states

Lyman ground state n = 1 UltravioletBalmer ground state n = 2 VisiblePaschen ground state n= 3 Infrared

QUANTUM MECHANICS:So far we have discussed light as a wave Einstein will return to Newton’s idea that it can also act as a particle. Einstien collected data proposing that light could be described as quanta of energy called photons and that these quanta acted as if they were particles. This was known as the Dual Wave-Particle behavior of light.

In 1924, Louis de Broglie asked, “Given that light behaves as a waves and particles, can particles of matter behave as waves?

Clinton Davisson and Lester Germer later backed de Broglie’s idea with experimentation. All objects have wave-like properties however the mass of the object must be very small in order for its wavelength to be large enough to observe. Classical mechanics describe the macro world while quantum mechanics describes the subatomic world.

Photoelectric effect The photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation such as x-rays or visible light.[1] The emitted electrons can be referred to as photoelectrons in this context. The effect is also termed the Hertz Effect[2][3], due to its discovery by Heinrich Rudolf Hertz, although the term has generally fallen out of use.

Study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave–particle duality.[1]

By the law of conservation of energy, the electron absorbs the energy of the photon and if sufficient, the electron can escape the material with a finite kinetic energy. A single photon can only eject a single electron because the energy of one photon can only be absorbed by one electron. The electrons that are emitted are often termed photoelectrons.

Electron microscopes use the wavelike properties of beams of electrons to magnify objects.

The Heisenberg Uncertainty Principle: States that it is impossible to know exactly both the velocity and the position of a particle at the same time. This is critical to the study of small particles like electrons but not for cars or planes.

So let us review the four principle quantum numbers.

1. The principle quantum number – n – - can have any integer value from 1 to infinity - it is primary to determining the energy of an electron - it is a measure of the size of the orbital greater n, greater orbital size2. The Angular Momentum Quantum Number – l – - each value of l corresponds to a different orbital shape - the value of n limits the number of subshells - l can be no larger than n-1 - so that 0 is an s, 1 is a p, 2 is a d, and 3 is an f - so an electron with a l = 1 is a p subshell inversely an electron in a p subshell has a value of 1

3. The Magnetic Quantum Number – m – - specifies to which orbital within a subshell the electron is assigned - orbitals in a given subshell differ only in their orientation in

space around the nucleus of the atom - the value of l limits the values of m, where m ranges from +l

to –l including 0 – ex. l = 2 then m = 2,1,0,-1,-2 - therefore when l = 2 (a d sublevel) there are five orbitals4. The Spin Quantum Number – s – - distinguishes the two electrons in an orbital - the first electron moving clockwise is considered +1/2 - the second electron moving counterclockwise is -1/2 - the electron occupy the same orbital - there are no more than two electrons in any given orbital