Chapter 7: Quantum Theory & Electronic Structure of Atoms

Photoelectric Effect

-Solved by Einstein: He suggested that a beam of light is really a stream of particles. These particles of light are now called photons. Using Planck's quantum theory of radiation as a starting point, Einstein deduced that each photon must possess energy E E= hv v=frequency of light -A phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency, called the threshold frequency. -The number of electrons ejected was proportional to the intensity (or brightness) of the light, but the energies of the ejected electrons were not. -Below the threshold frequency no electrons were ejected no matter how intense the light.

Pauli Exclusion Principle

-To determine electron configurations -This principle states that no two electrons in an atom can have the same set of four quantum numbers. If two electrons in an atom should have the same n, ℓ, and mℓ values (that is, these two electrons are in the same atomic orbital), then they must have different values of ms. In other words, only two electrons may occupy the same atomic orbital, and these electrons must have opposite spins

Heisenberg Uncertainty Principle

It is impossible to know simultaneously both the momentum p (defined as mass times velocity) and the position of a particle with certainty.

Difference in line spectra and continuous spectra

Line spectra: the light emission only at specific wavelengths Continuous spectra: the light emitted goes along the entire spectrum

s, p, and d orbital

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Speed (u) of a wave

u= (λ)(v)

Convert wavelength to frequency

v = c/λ, frequency = speed of light/ wavelength

First 10 elements has revealed about ground-state electron configurations and the properties of electrons in atoms

1) No two electrons in the same atom can have the same four quantum numbers. This is the Pauli exclusion principle. 2) Each orbital can be occupied by a maximum of two electrons. They must have opposite spins, or different electron spin quantum numbers. 3) The most stable arrangement of electrons in a subshell is the one that has the greatest number of parallel spins. This is Hund's rule. 4) Atoms in which one or more electrons are unpaired are paramagnetic. Atoms in which all the electron spins are paired are diamagnetic. 5) In a hydrogen atom, the energy of the electron depends only on its principal quantum number n. In a many-electron atom, the energy of an electron depends on both n and its angular momentum quantum number ℓ. 6) In a many-electron atom the subshells are filled in the order. 7) For electrons of the same principal quantum number, their penetrating power, or proximity to the nucleus, decreases in the order s > p > d > f. This means that, for example, more energy is required to separate a 3s electron from a many-electron atom than is required to remove a 3p electron.

Speed of light (c)

3.00 x 10^8 m/s

Wavelength range of visible spectrum

400nm (violet) to 700 nm (red)

General Rules for Assigning Electrons to Atomic Orbitals

Based on the preceding examples we can formulate some general rules for determining the maximum number of electrons that can be assigned to the various subshells and orbitals for a given value of n: 1) Each shell or principal level of quantum number n contains n subshells. For example, if n = 2, then there are two subshells (two values of ℓ) of angular momentum quantum numbers 0 and 1. 2) Each subshell of quantum number ℓ contains (2ℓ + 1) orbitals. For example, if ℓ = 1, then there are three p orbitals. 3) No more than two electrons can be placed in each orbital. Therefore, the maximum number of electrons is simply twice the number of orbitals that are employed. 4)A quick way to determine the maximum number of electrons that an atom can have in a principal level n is to use the formula 2n2.

Paramagnetic vs. Diamagnetic

Paramagnetic substances are those that contain net unpaired spins and are attracted by a magnet. On the other hand, if the electron spins are paired, or antiparallel to each other (↑↓ or ↓↑), the magnetic effects cancel out. Diamagnetic substances do not contain net unpaired spins and are slightly repelled by a magnet.

Photons

Particles of light

Aufbau Principle

Protons are added one by one to the nucleus to build up the elements, electrons are similarly added to the atomic orbitals

Regions of the electromagnetic spectrum from highest to lowest wavelength

Radiowaves (highest wavelength) Microwave Infrared Visible Ultra-violet X-rays Gamma rays (lowest wavelength)

Noble Gas Core

Shows in brackets the noble gas element that most nearly precedes the element being considered, followed by the symbol for the highest filled subshells in the outermost shells.

Hund's Rule

States that the most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. The arrangement shown in (c) satisfies this condition.

The four quantum numbers

The four quantum numbers

Schrödinger's Quantum Mechanics Model of Atomic Structure

Wave function (psi): The probability of a particle's quantum state as a function of position, momentum, time, and/or spin. Depends on the location in space of the system. Electron density: Gives the probability that an electron will be found in a particular region of an atom. Atomic orbital: the wave function of an electron in an atom. Quantum numbers: Describe the distribution of electrons in hydrogen and other atoms Shell: A collection of orbitals with the same value of n is frequently called a shell. Subshell: One or more orbitals with the same n and ℓ values are referred to as a subshell

Characteristics of an electromagnetic wave

Wavelength λ (lambda): the distance between identical points on successive waves. Frequency v (nu): the number of waves that pass through a particular point in 1 second. Amplitude: the vertical distance from the midline of a wave to the peak or trough.