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AP Chemistry NOTES 13-1

ATOMIC STRUCTURE & MASS SPECTROMETRY

Fractional abundance – the fraction of a quantity of an element that is composed of a particular isotope For instance, the fractional abundances of the isotopes in neon are as follows: Isotope Fractional Abundance Percent Abundance Neon-20 0.9051 90.51 % Neon-21 0.0027 0.27 % Neon-22 0.0922 9.22 % Note that the atomic weight (or atomic mass) of neon is close to 20 due to the high fractional abundance of the Neon-20 isotope. This atomic mass can be calculated precisely:

Average Atomic Mass = 20(0.9051) + 21(0.0027) + 22(0.0922) = 20.1871 amu Mass Spectrometry –a method of determining the masses of atoms by measuring the mass-to-charge ratios of

the positively charged ions formed from these atoms by the mass spectrometer; different isotopes are separated by a magnetic field, causing them to land in different positions on a detector.

Mass Spectrum of Boron

The atomic mass may be calculated from a measurement of the relative heights of the peaks from a mass spectrum, which represent the fractional abundances:

Height of line at 10 = 1.1 cm Height of line at 11 = 4.9 cm Total height = 6.0 cm

Fractional Abundance of 10B = 1.1/6.0 = 0.1833 Fractional abundance of 11B = 4.9/6.0 = 0.8167

Atomic mass of Boron = 0.1833(10) + 0.8167(11) = 10.8163 amu

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AP Chemistry NOTES 13-2

THE DUAL NATURE OF LIGHT

ELECTROMAGNETIC RADIATION Electromagnetic Radiation – the type of energy that travels through space in the form of waves

composed of oscillating electric and magnetic fields

The speed of an electromagnetic wave is related to its wavelength and frequency according to the following equation:

c = λν where c = 3.00 x 108 m/s λ = wavelength (in meters) ν = frequency (in s-1 or Hertz) THE QUANTIZED NATURE OF LIGHT Until the end of the 19th century, it was believed that matter could absorb or emit any quantity of energy. Max Planck (upon working with and studying the radiation “profiles” of solid bodies heated to incandescence) discovered that energy was only gained or lost in whole number multiples of the quantity “hv”:

∆E = hν where E = energy (in Joules)

h = Planck’s Constant (6.626 x 10-34 J . s) ν = frequency (s-1 or Hertz)

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This meant that the energy associated with matter was not continuous, but was in fact “quantized” – it occurs in discrete “hv” units or packets of energy called “quanta”. The next important discovery came from Albert Einstein when he suggested that electromagnetic radiation

can be viewed as a stream of “particles” called photons (a small particle of light energy). Einstein combined these first two equations and obtained the following:

Ephoton = hν = hc λ or

E = hc λ THE DUAL NATURE OF LIGHT

At the end of the 19th century, it was thought that matter and energy were distinct: 1. Matter consisted of particles. 2. Radiant energy was in the form of waves. 3. Particles had mass and a specified position. 4. Waves were massless and delocalized. Matter and energy did not intermingle. Work done my Max Planck, however, began a series of discoveries that proved this theory to be incorrect (ie. his work with the quantum nature of light). In addition, Albert Einstein’s concept of “photons” shed more light (no pun intended) on the mass/energy relationship. In a related mental leap, Albert also developed his “signature” equation, which he published in his “Special Theory of Relativity” in 1905:

E = mc2 The major point of this equation:

ENERGY HAS MASS!!

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Rearranging the above two equations, the mass of a photon of light of a particular wavelength can be determined:

m = E = hc/λ = h c2 c2 λc or

m = h λc

EXAMPLE: Calculate the mass of a photon of light with a wavelength of 650 nm. Does a photon really have mass??? The answer appears to be yes!! Subsequent experiments have verified this postulate. (Note: The mass of a photon at rest is thought to be zero, although we have never observed one at rest.***) This apparent wave/particle composition of light is often referred to as the dual nature of light. THE DUAL NATURE OF MATTER??? If light energy has properties of both waves and particles, could the opposite be true? Does matter exhibit wave-like properties?

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Louis de Broglie (in 1923) revised the above equation to include particles of matter at any velocity (not just the speed of light):

m = h λυ or

λ = h mυ

where m = mass (in “kg”)

h = Planck’s constant (6.626 x 10-34 kg.m2/s) (note the change in units) λ = wavelength (in meters) υ = velocity (in m/s) This equation is known as the “de Broglie Equation”. EXAMPLE: Compare the de Broglie wavelength for an electron (mass = 9.11 x 10-31 kg) traveling at a speed

of 1.0 x 107 m/s with that for a ball (mass = 0.10 kg) traveling at 35 m/s. This wavelength for an electron has been verified experimentally. The wavelength of a ball is so small, it is impossible to verify, but the postulate remains:

1. Large pieces of matter (such as baseballs) exhibit mostly particle properties while wave-like properties are too small to measure.

2. Very small pieces of matter (photons) exhibit mostly wave-like properties, but also exhibit some

particle properties. 3. Particles of intermediate size (electrons) clearly exhibit both particle and wave-like properties. Watch this: Quantum Mechanics

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AP Chemistry NOTES 13-3 ENERGY AND ELECTRONS

ATOMIC LINE SPECTRA AND THE BOHR MODEL After the discovery of the electron by Thomson, and the nucleus by Rutherford, many scientists believed we had discovered all there was to know about the atom. Neils Bohr, however, wasn’t satisfied. He applied some of the work that had already been done in physics and postulated that the electrons weren’t just haphazardly strewn around the nucleus, but instead were located in very specific energy levels that he could predict mathematically (at least for the hydrogen atom. One area of physics and chemistry that was just being explored – that of “atomic line spectra” – backed up his theory. When an object is heated, it can glow or give off radiation. There are millions of different frequencies produced, so this emitted light (when seen through diffraction grating or a spectroscope, etc.) is a continuous spectrum. However, when a single element (ie. a gas) is heated, it gives off very distinct, often separated frequencies that appear as individual “lines” in the spectrum. This “emission spectrum” or “bright line spectrum” backed up Bohr’s concept of energy levels for the electrons in the atom. The electron in the hydrogen atom is normally in its “ground state” at the lowest possible energy level (n = 1), but when excited by absorption of energy, it will “leap” to higher energy levels (a very unstable state). The electrons will immediately hop back down to lower energy levels, emitting energy in very distinct amounts.

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Rydberg found that the wavelength of these lines – representing a hop from a higher energy level (ni) to a lower energy level (ni) – could be predicted using the following equation (known as the Rydberg Equation):

𝟏

𝛌= 𝐑 (

𝟏

𝐧𝐟𝟐

− 𝟏

𝐧𝐢𝟐

)

where R = 1.09737 x 107 m-1 λ = wavelength (meters) EXAMPLE: What wavelength of light (in nm) is produced when an electron in the hydrogen atom “hops”

from the fourth energy level to the second energy level?

What region of the electromagnetic spectrum is this? ________________________________________ To which series of the electron transitions in the hydrogen atom does this wavelength belong? (See handout for a diagram showing the Lyman Series, Balmer Series, and Paschen Series of electron transitions for the hydrogen atom.)

_____________________________________

The energy of an electron at a specific energy level in the hydrogen atom can be calculated as follows:

𝐄𝒏 = −𝐑𝐡𝐜

𝒏𝟐 𝒐𝒓 𝐄𝒏 =

−𝟐. 𝟏𝟕𝟖 𝐱 𝟏𝟎−𝟏𝟖𝐉𝐨𝐮𝐥𝐞𝐬

𝒏𝟐

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For electron transitions:

𝚫𝐄 = −𝟐. 𝟏𝟕𝟖 𝐱 𝟏𝟎−𝟏𝟖 𝐉 (𝟏

𝐧𝐟𝟐

− 𝟏

𝐧𝐢𝟐

)

EXAMPLE: The Paschen series of lines in the hydrogen spectrum occurs in the infrared region. The electrons that produce them are moving from higher states to the n=3 state. Give ni for the least energetic line of the series:_________

What is the energy involved in the least energetic transition? What are the frequency and wavelength of the emitted light?

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AP Chemistry NOTES 13-4

ELECTRON CONFIGURATION & PERIODIC TRENDS

ELECTRON STRUCTURE AND MAGNETISM When an electron spins, a magnetic field is induced around that electron. Another electron spinning in the opposite direction would have an opposing magnetic field. This phenomenon is responsible for the magnetic properties of the elements: *Diamagnetic - Describes substances which are not attracted by a magnet, but are in fact slightly repelled by one (ie. chalk, sugar, etc.) Results when atoms contain electrons that are all paired up (thereby “canceling” their magnetic fields) *Paramagnetic – Describes substances which are attracted to a magnetic field. Results when elements contain unpaired electrons (which all spin in the same direction, “concentrating” the field) *Ferromagnetic – Describes substances which remain magnetic, even after being removed from a magnetic field PERIODIC TRENDS (Focus on Fluorine) *Nuclear Charge (Z) – the total charge of all of the protons in the nucleus *Electron Shielding – the decrease in attraction between an electron and the nucleus caused by the “charge blocking” effect of the inner core electrons(

*Core Electrons (σ) – electrons in lower energy levels

1. Atomic Radius – half the distance between the nuclei in a molecule consisting of identical atoms: a) Tends to decrease as you move across the periodic table

Valence electrons are being added into the same shell. Since the nuclear charge is increasing (but no additional electron shielding), the valence electrons feel a greater attraction to the nucleus and are pulled in somewhat

b) Tends to increase as you move down the periodic table Electrons are added into higher energy levels (increased electron shielding from core electrons) so the outer electrons are attracted less strongly; there is also more e- - e- repulsion so the

electrons spread out more

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EXAMPLE: Which is larger? Why?

Calcium or Strontium

Sodium or Magnesium

NOTE: For Ions – *Positive Ions are always smaller than their neutral counterparts *Negative Ions are always bigger than their neutral counterparts 2. Ionization Energy – the energy required to remove an electron from a gaseous atom or ion:

X(g) → X+(g) + e-

a) I1 (first ionization energy) tends to decrease as you move down the periodic table.

*There is more electron shielding (due to the inner “core” electrons) on the outermost electron as you move down the table since electrons are being added into higher energy levels

*The outermost electron is in a higher energy level as you move down the table, and therefore

requires less energy to remove b) I1 (first ionization energy tends to increase as you move across the periodic table.

*The valence electrons for the atoms are in the same shell as you move across the periodic table (and so the electron shielding remains the same). However, the nuclear charge is increasing as you move across the table, so the valence electrons experience an increasing attraction for the nucleus, and therefore require a higher amount of energy to remove.

EXAMPLE: Why is the first ionization energy for fluorine greater than that of carbon?

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EXAMPLE: Why is the first ionization energy for phosphorous lower than that of nitrogen? EXAMPLE: Explain the following. *I1 of boron is less than I1 of beryllium EXAMPLE: The first ionization energy for phosphorus is 1060 kJ/mol, and that for sulfur is 1005 kJ/mol. Why? EXAMPLE: Consider atoms with the following electron configurations: 1s22s22p6 1s22s22p63s1 1s22s22p63s2

Which has the largest I1? Why? Which has the smallest I1? Why?

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EXAMPLE: Analyze the following. Al(g) → Al+(g) + e- I1 = 80 kJ/mol Al(g)

+ → Al2+(g) + e- I2 = 1815 kJ/mol

Al(g)

2+ → Al3+(g) + e- I3 = 2740 kJ/mol

Al(g)

3+ → Al4+(g) + e- I4 = 11,600 kJ/mol

Explain: The small value for I1 The very large value for I4 3. Electron Affinity – the energy absorbed when an electron is added to a gaseous atom (By convention, the easier to add an electron, the more negative the value for electron affinity) a) Becomes more negative as you move across the periodic table Increased nuclear charge, but fairly constant electron shielding, increases the attraction for electrons (and makes it a more “exothermic” process – hence the negative charge) b) Becomes less negative as you move down the periodic table The electrons are further away from the nucleus and therefore feel less attraction (increased electron shielding from core electrons) so more energy is needed to add an electron (more “endothermic”)

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4. Electronegativity – the tendency of an atom to attract shared electrons to itself a) Tends to increase as you move across the periodic table

Valence electrons are being added into the same shell. Since the nuclear charge is increasing (but no additional electron shielding), the valence electrons feel a greater attraction to the nucleus

b) Tends to decrease as you move down the periodic table

Electrons are added into higher energy levels, which are further away from the nucleus. Therefore, the valence electrons are attracted less strongly.

EXAMPLE: Which of the following has the higher electronegativity value? Why?

Carbon or Nitrogen

Sodium or Potassium

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AP Chemistry NOTES 13-5

PHOTOELECTRON EMISSION SPECTROSCOPY (PES)

PHOTOELECTRIC EFFECT – the observation that many metals will emit electrons when bombarded with

photons of light; this is the principle behind solar cells

PHOTOELECTRON SPECTROSCOPY (PES) – uses the information from the energy of the electrons emitted by the photoelectric effect to gain information about the electron structure of a substance

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An example of the information gained from this device is shown below, with the photoelectron spectrum of

hydrogen:

The energy shown for the electron is in electron volts (eV), and is the amount of energy required to remove

the electron from the atom. Spectra for the first 21 elements can be found using the following link:

http:// www.chem.arizona.edu/chemt/Flash/photoelectron.html.

Notice that as the number of electrons at a particular energy increase, the size of the peak increases.

In addition, since the energy given is the “ionization energy” – the amount of energy required to remove an electron

from an atom, the higher the energy on the photoelectronic emission spectrum, the lower the energy level location of

that electron around the nucleus of the atom. Remember, it requires more “energy rope” to remove an electron that is

at a lower energy level in the atom.

Energy “rope” for n=2 electron

Energy “rope” for n=1 electron

Energy “rope” for n=3 electron

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Notice what happens with

Scandium:

This is our first instance of “overlapping”.