How are subatomic particles arranged in an atom?

Rutherford’s Scattering Experiment:

· Experimental set-up: Positively charged particles (alpha) were focused at a thin (0.00004 cm) sheet of gold foil.

· Expectation: The alpha particles would scatter as they were deflected by the gold atoms, producing a pattern similar to spray from a nozzle.

Surprise!

· Observation 1: Most alpha particles passed straight through the gold foil.

Conclusion: Volume taken up by atoms is mostly empty space.

· Observation 2: A few alpha particles bounced back toward the source.

Conclusion: Particles must have hit something that was tiny, dense and electrically charged.

Rutherford named the tiny, dense, positively charged region at the center of the atom the nucleus.

· Protons and neutrons are found in the nucleus. Electrons occupy a large region of space around the nucleus (electron cloud) and are in motion.

· Atomic number: number of protons. Each element has a different atomic number.

· Elements in the periodic table are listed according to increasing atomic number.

· Mass number: total number of protons and neutrons in nucleus of an atom

· Average atomic mass: weighted average of the masses of all the different isotopes of an element

Example:

Isotopes: Atoms of an element containing different numbers of neutrons

Existence of isotopes often causes the atomic mass listed in the periodic table to be a mixed number, indicating the weighted average of the masses of all the different isotopes of this element.

Example:

Isotopes are commonly symbolized in two ways:

1) The mass number is used to identify the isotope (e.g. Hydrogen-3, Carbon-14, etc.)

2) An isotope symbol is used to identify the isotope.

Write an isotope symbol for carbon-14:

Practice Problems:

1) Your chemistry course requires that you take five quizzes throughout the course of the semester. Each quiz is worth 10 points, and you receive the following scores on your quizzes:

Quiz 1: 9/10 Quiz 2: 6/10

Quiz 3: 6/10 Quiz 4: 9/10

Quiz 5: 6/10

• What percentage of the time did you receive a 9/10?

• What percentage of the time did you receive a 6/10?

• What is the weighted average of your quiz scores?

Two approaches:

2) Naturally occurring carbon consists of 98.892% Carbon-12 (atomic mass = 12.0000 atomic mass units) and 1.108% Carbon-13 (atomic mass = 13.00335 amu). Calculate the weighted average of these two isotopes of carbon.

3) Boron has an average atomic mass of 10.81 atomic mass units and consists of two stable isotopes: Boron-10 with an atomic mass of 10.0129 amu and Boron -11 with an atomic mass of 11.0093 amu.

Calculate the percent abundance of each isotope. (Hint: Use your knowledge of algebra and set up two equations involving the two unknowns.)

4) Naturally occurring chlorine consists of two isotopic forms, Chlorine-35 and Chlorine-37. Which of these two is more abundant?

Arrangement of Electrons in Atoms

An element's properties are determined largely by the number of electrons in its atoms and how these electrons are arranged.

The Bohr Model:

· Electrons occupy different energy levels in the space surrounding an atomic nucleus.

· Electrons under normal circumstances maintain the lowest possible energy level.

(Ground state or unexcited state)

· Electrons can absorb energy and “jump” to a higher energy level.

(Excited state)

· When returning to the ground state, the electron gives off energy as a particular blend of colors.

· Separating this blend of colors produces an element's line spectrum (i.e. fingerprint).

· The energy difference between levels is specific to a given element, resulting in a specific color emission:

Element Color

K lavender

Ca orange-red

Na yellow

Ba green

· The significance of line spectra is that energy can be given off or absorbed only in definite amounts (quanta).

· These specific amounts of energy relate to differences between energy levels:

· Electrons occupy the lowest energy level available until it is full.

· The reactivity of elements is due to the number of electrons in the outermost energy level (valence electrons).

· The construction of the periodic table indicates the number of valence electrons for each element.

Examples: Sodium (Na); Chlorine (Cl)

Electromagnetic radiation

All types of radiant energy can be described as waves, with a specific wavelength (l) and frequency (n).

· The speed at which the wave is travelling is equal to the wavelength times the frequency.

ln = c

· Light corresponds to a portion of the electromagnetic spectrum, and c represents the speed of light, 3.00 ´ 10⁸ m/s.

· When passed through a prism, white light can be separated into a continuous spectrum of colors: ROYGBIV.

· Frequency and wavelength change with the progression of colors. Red (l ~ 7´10^-7 m, n ~ 4.3´10¹⁴ Hertz), Violet (l ~ 4´10^-7 m, n ~ 7.5´10¹⁴ Hertz)

· 1 Hertz = 1/s = 1 s^-1

· 1 Angstrom (A) = 1´10^-10 m

· Light can also be described as composed of particles called photons, with each photon having a particular amount (quantum) of energy.

· The energy of a photon of light is given by Planck’s equation:

E = hn or E = hc/l

· Planck’s constant = h = 6.6262´10^-34 J·s

· Energy is directly proportional to frequency and inversely proportional to wavelength.

The red color in many fireworks is due to the emission of light from strontium salts. Calculate the frequency of a photon of light of wavelength 6.50´10³ A. Also calculate the energy in kJ for one mole of these photons.

ln = c E = hn

In the 19^th century J. R. Rydberg developed an equation based on observations showing a relationship between the wavelengths of the lines in the hydrogen line spectrum.

1/l = R (1/n₁² – 1/n₂²)

R = Rydberg constant = 1.097´10⁷ m^-1

n₁ and n₂ are integers such that n₂>n₁

Niels Bohr further explained this relationship by suggesting that n₁ and n₂ represent energy levels where electrons can exist in the hydrogen atom.

· He assumed that these levels corresponded to quantized amounts of energy, so that electrons could only exist at these levels and must absorb or emit a specific amount of energy to move to a different level.

· Bohr described these energy levels as circular orbits around the nucleus.

Calculate the wavelength and energy of a photon of light needed to promote an electron from the 1^st energy level to the 4^th energy level in a hydrogen atom.

Rydberg’s equation and Bohr’s model are able to explain the behavior of an electron in a one electron species (H atom, He⁺ ion, etc.), but do not explain more complex species.

· A more accurate explanation of how electrons are arranged and what types of transitions are possible is needed.

· Electrons in atoms behave more like waves than particles.

Heisenberg Uncertainty Principle:

It is impossible to determine accurately both the momentum and the position of an electron simultaneously.

Instead, we can describe the probability of finding an electron within a specific region, using quantum numbers.

· Atomic orbital: a region of space where there is a high probability of finding an electron.

· Quantum numbers are used to describe electrons in possible atomic orbitals.

Principal quantum number (n) … describes the main energy level in which the electron is found

· Possible values: n = 1, 2, 3, 4, etc. with each level existing further out from the nucleus

Subsidiary quantum number (l) … describes the shape of atomic orbital; these shapes are referred to as sublevels

· Possible values within a main energy level: l = 0, 1, 2, … (n – 1)

· Energy level n=1 has 1 sublevel (l =0)

Energy level n=2 has 2 sublevels (l =0, 1)

Energy level n=3 has 3 sublevels (l =0, 1, 2)

Energy level n=4 has 4 sublevels (l =0, 1, 2, 3)

· Sublevel l = 0 is a “s” sublevel (spherical)

Sublevel l = 1 is a “p” sublevel (hour glass)

Sublevel l = 2 is a “d” sublevel

Sublevel l = 3 is a “f” sublevel

· Relative arrangement of s sublevels: Fig 5-20

Magnetic quantum number (m_l) …describes the spatial orientation of an atomic orbital

· Possible values within a sublevel:

m_l = - l , …, 0, …, l

· s sublevels have 1 possible orientation (m_l = 0)

p sublevels have 3 possible orientations (m_l = -1, 0, 1)

d sublevels have 5 possible orientations (m_l = -2, -1, 0, 1, 2)

f sublevels have 7 possible orientations (m_l = -3, -2, -1, 0, 1, 2, 3)

Spin quantum number (m_s) … describes the spin of an electron and the orientation of the magnetic field produced by the spin.

· Possible values: m_s = -½, ½

Atomic orbitals can accommodate a maximum of two electrons, each with opposite spin.

· Electrons in the same orbital with opposite spins are spin-paired, often called paired.

How many orbitals exist and how many electrons can fit in …

Level 1?

Level 2?

Level 3?

Level 4?

Energy

Level Sublevel Orbitals Electrons

n = 1 s 1 2

n = 2 s, p 1+3=4 8

n = 3 s, p, d 1+3+5=9 18

n = 4 s, p, d, f 1+3+5+7=16 32

The Aufbau principle provides a guideline for the order in which orbitals fill. It is a general guideline, but several exceptions occur for specific elements.

Orbitals fill based on their relative energy, with orbitals increasing in energy as n increases and as l increases within a level n. Orbitals within a sublevel are equal in energy (degenerate).

The usual order of energies is as shown below. Remember, exceptions to this order do occur.

Pauli Exclusion Principle: No two electrons in an atom may have identical sets of four quantum numbers.

Hund’s Rule: Electrons must occupy all orbitals of a given sublevel before electron pairing begins. These unpaired electrons have parallel spins.

Orbital Notations

Identity	1s	2s	2p	Electron configuration	Simplified configuration
H	h			1s^1	1s^1
He	hi			1s^2	1s^2
Li	hi	h		1s^22s^1	[He]2s^1
Be	hi	hi		1s^22s^2	[He]2s^2
B	hi	hi	h	1s^22s^22p^1	[He]2s^22p^1
C	hi	hi	h h	1s^22s^22p^2	[He]2s^22p^2
N	hi	hi	h h h	1s^22s^22p^3	[He]2s^22p^3
O	hi	hi	hi h h	1s^22s^22p^4	[He]2s^22p^4
F	hi	hi	hi hi h	1s^22s^22p^5	[He]2s^22p^5
Ne	hi	hi	hi hi hi	1s^22s^22p^6	[He]2s^22p^6

For continuation through Kr, see pp. 194-195.

· Note electron configurations and orbital notations mostly follow the Aufbau principle.

· Note exceptions to expected order of filling in Cr and Cu – half-filled and filled sets of equivalent orbitals have a special stability.

· Noble gases are very unreactive and have ns²np⁶ configurations (except He) – often oversimplified as “a full outer shell”

Write an acceptable set of quantum numbers, an orbital notation, an electron configuration, and a simplified configuration to describe the arrangement of electrons in a nitrogen atom.

Electrons

n