Quantum Theory of the Atom

Flashcards covering the wave nature of light, quantum effects, Bohr's theory, and the fundamentals of quantum mechanics and quantum numbers based on lecture notes.

Wave

A continuously repeating change or oscillation in matter or in a physical field.

Electromagnetic Wave

A wave consisting of oscillations in electric and magnetic fields traveling through space.

Wavelength ($\lambda$)

The distance between any two identical points on adjacent waves.

Frequency ($\nu$)

The number of wavelengths that pass a fixed point in one unit of time, usually measured in Hertz ($Hz$) or $s^{-1}$.

Speed of Light ($c$)

The wave speed for light, equal to $3.00 \times 10^8\,m/s$, related to wavelength and frequency by the equation $c = \nu\lambda$.

Electromagnetic Spectrum

The entire range of frequencies and wavelengths of electromagnetic radiation.

Diffraction

The property of waves where they spread out when they encounter an obstacle about the size of their wavelength.

Planck's Constant ($h$)

A fundamental constant assigned a value of $6.63 \times 10^{-34}\,J \cdot s$ used in the energy formula $E = h\nu$.

Quantized

The property of having only specific, allowed values, such as the vibrational energies of atoms which can only be $h\nu$, $2h\nu$, $3h\nu$, etc.

Photoelectric Effect

The ejection of electrons from the surface of a metal when light exceeding a certain threshold frequency shines on it.

Photon

A particle of light proposed by Einstein that carries energy proportional to its frequency ($E = h\nu$).

Wave-Particle Duality of Light

The concept that light displays characteristics of both waves (frequency) and particles (photons).

Continuous Spectrum

A spectrum that contains all wavelengths of light.

Line Spectrum

A spectrum showing only certain colors or specific wavelengths of light, produced when atoms are heated.

Energy-Level Postulate

Bohr's idea that an electron can have only certain quantized energy values, given for hydrogen by $E_n = -R_H / n^2$.

Rydberg Constant ($R_H$)

A constant used in calculating the energy of an electron in a hydrogen atom, valued at $2.179 \times 10^{-18}\,J$.

Atomic Absorption

The process where an atom takes in light to move an electron from a lower energy level to a higher energy level ($n_f > n_i$), resulting in a positive $\Delta E$.

Atomic Emission

The process where an atom releases light as an electron moves from a higher energy level to a lower energy level ($n_f < n_i$), resulting in a negative $\Delta E$.

Quantum Mechanics

The branch of physics that mathematically describes the wave properties of submicroscopic particles like electrons.

Heisenberg's Uncertainty Principle

A principle stating it is impossible to know both the exact position ($\Delta x$) and momentum ($m\Delta v_x$) of a particle simultaneously.

Wave Function ($\psi$)

A mathematical expression defined by Erwin Schrodinger that describes the probability of finding an electron at a given point around the nucleus.

Atomic Orbital

A wave function described by three quantum numbers ($n$, $l$, $m_l$) that representing a region of space with a high probability of finding an electron.

Principal Quantum Number ($n$)

The quantum number on which the energy of an electron primarily depends, defining the energy level or shell ($n = 1, 2, 3, \dots$).

Angular Momentum Quantum Number ($l$)

The quantum number that distinguishes subshells of different shapes, with values from $0$ to $(n - 1)$, denoted as $s$, $p$, $d$, and $f$.

Magnetic Quantum Number ($m_l$)

The quantum number that distinguishes orbitals of a given energy and shape but having different orientations, with values from $-l$ to $+l$.

Spin Quantum Number ($m_s$)

The quantum number referring to the two possible orientations of an electron's spin axis, with values of $+1/2$ or $-1/2$.

s Orbital

An atomic orbital that is spherical in shape.

p Orbital

An atomic orbital consisting of two lobes along a straight line through the nucleus.

Electronegativity trend down a group

Decreases. Each new shell adds more distance and electron shielding between the nucleus and bonding electrons, so the nucleus attracts shared electrons less effectively.

Electronegativity

Pull of an atom to its bonding electrons

Ionization energy

The energy required to remove a valance electron

Atomic radius

1/2 of the distance between a nuclei of two identically bonded atoms

Emission spectra

Pattern in which certain elements emit light

When elements are heated they emit light in a line spectrum based on the lights frequency

Line spectrum

Shows only certain colors/specific wavelengths of light

continuous spectrum

All Wavelength/frequencies of light, rainbow

Basis of the Bohr model

Electrons remain in fixed, orbits and transferred between orbits and discrete jumps, releasing and absorbing energy

Only works for H

Ground state

The lowest energy level/state and electron would exist at

Excited state

Highest energy level/state electron would exist at

Changes and energy level/states

Positive change in energy; when energy is absorbed, when electron is excited

Negative change and energy; when energy is released as photons, when electron falls back to ground state

Continlus

Equation to show change and energy/jump of electrons

E=- RH/n²

E=joules

Rydberg equation

Change in energy = RH (1/n²i-1/n²f)

Shows change of energy of electrons as it moves between energy levels

The sign of change in energy shows the direction of the energy because frequency and wavelength can’t be negative

Change in energy is equal to the energy of the photon

Effective nuclear charge

The pool that the nucleus has on an outer electron, it is lower than the number of protons because the core electrons block the full strength of the nucleus

Quantum theory

Describing the behavior of matter and energy at atomic and sub, atomic scales, particles behave like waves and exist in photons

Origins of quantum theory

Plancks discovery of photons with the photoelectric effect

Quantum mechanics

Branch of physics, that mathematically describes wave properties of sub microscopic particles

Electron affinity

The energy change that occurs an electron is acquired by a neutral atom makes an anion

History and development of the periodic table

Mendeleev made the first periodic table which was grouped by properties

Mostly defined atomic number and arranged the table by that

Newland made the law of octanes

Mendeleev

He organized elements by properties and looked for trends

Saw that when the elements were arranged by atomic weight, they were grouped in similar properties

Created first periodic table 1869

Left empty space is in periodic table for future elements to be discovered

Henry Mosley

1911

Found a pattern of nuclear charge in the number of protons creating the modern definition of atomic number

John newlands

Proposed the law of octanes

When elements are arranged by increasing atomic weight, every eighth element would have similar properties

This law broke down after calcium on the table, but remains true for periods 2 and 3

Effective nuclear charge

The pulling force valance electrons actually feel by the nucleus

This is lower than the actual force of the nucleus because of the shielding affect of the core electrons

Periods: increases across (same amount of core electrons so effect is the same but there and more ve and p)

Group: stay about the same

Ionization trends

periods: increase across periods

-as you add protons and electrons the same energy levels there is a stronger effective nuclear charge meaning there’s a stronger pull on the electrons inward

Groups: decrease

As you add energy levels the valence electrons become farther from the nucleus

Electronegativity trends

Periods: increase across periods

• as you add protons and electrons in the same energy level the effect nucleus charge increases

The stronger the nucleur charge pulls the shared bonded electrons inward toward the nufelus

groups: decrease down groups

As you add energy levels, the valence electrons become farther from the nucleus so the effective nuclear charge is decreasing in the atom/nucleus is not attracting electrons as well

Atomic radius trends

Periods: decrease across a period

as you add protons and electrons in the same energy level the nucleur charge increases and pulls valence electrons inward

group: increases down a group

As you add energy levels the size of the atom increases and you increase the distance beteeen p and ve