Atomic Physics K K Dey Assistant Professor in Physics B B College, Asansol

hydrogen atom It is the simplest atomic system.

Why is it important to study the hydrogen atom? The hydrogen atom is an ideal system for relating theory to experimentation. Much that we learn about hydrogen can be extended to single electron ions like He and Li. Studying the quantum numbers for the allowed states of hydrogen will help us to describe the allowed states of more complex atoms.

Early Models Of The Atom The Greek model Tiny, hard, indestructible sphere

The J. J. Thomson model A volume of positive charge is embedded with negative charges called “electrons”

The Rutherford model A positive nucleus orbited by electrons. The nucleus contains 99.9% of the atom’s mass

The Rutherford model Which force holds the electrons in orbit? The Coulomb force

Problems with the Rutherford Model There were two basic difficulties with the Rutherford model. It could not explain why atoms radiate discrete frequencies. Accelerating electrons should radiate electromagnetic waves.

Electron Transitions Using a high voltage to move electrons through a gas causes the gas electrons to become excited and to jump from lower energy levels to higher energy levels. Photons of various wavelengths are produced when electrons fall from higher energy levels to lower energy levels.

Emission Spectra The emission spectrum of hydrogen Can be produced by applying a high voltage across an evacuated glass tube filled with hydrogen The observed wavelengths are characteristic only of hydrogen

The Balmer Series In the Balmer Series nf = 2 There are four prominent wavelengths 656.3 nm (red) 486.1 nm (green) 434.1 nm (purple) 410.2 nm (deep violet)

Balmer Wavelengths

The Balmer Series Wavelength Equation RH is the Rydberg constant RH = 1.0973732 x 107 m-1

Two Other Important Series Lyman series (UV) nf = 1 Paschen series (IR) nf = 3

Spectral Lines How many different spectral lines could be produced by an electron in the n = 3 state? Three

Spectral Lines How many different spectral lines could be produced by an electron in the n = 4 state? Six

Photon Energy The equation for determining the energy of the emitted photon in any series:

The Absorption Spectrum An element can absorb the same wavelengths that it emits. The spectrum consists of a series of dark lines.

Identifying Elements The absorption spectrum was used to identify elements in the solar atmosphere were identified in this way. Helium was discovered.

Thermal vs. Atomic Spectra How could you tell if the light from a candle flame is thermal or atomic in origin?

If the spectrum is continuous, the source must be thermal.

Auroras What is the origin of the colors in the aurora borealis?

High speed particles from space interact with the earth’s magnetic field.

The Bohr Theory Of Hydrogen At the beginning of the 20th century, scientists wondered why atoms only radiated certain wavelengths. Bohr provided an explanation.

Four Assumptions of The Bohr Theory 1) The electron orbits the proton due to the Coulomb force which produces centripetal acceleration.

2) Only certain electron orbits are stable and do not radiate energy.

3) Radiation is only emitted when an electron drops from a more energetic state to a lower state.

4) The radius of the electron’s orbit is determined by the electron’s orbital angular momentum.

Total Energy of the Hydrogen Atom The total energy of the hydrogen atom can be determined by using this equation.

The Bohr Radius An electron can exist only in certain allowed orbits determined by the integer n. When n = 1, we have what is known as the Bohr radius (ao). ao = 0.0529 nm

Orbital Radii A general equation for finding the radius of any orbit:

Energy States The energy for various energy states can be found by using: n= 1 is the ground state

Ionization Energy The minimum energy required to ionize the atom is called the ionization energy. An electron is completely removed from the atom.

The Hydrogen Spectrum The general expression for determining wavelengths of the various series in the hydrogen spectrum

Bohr’s Correspondence Principle Quantum mechanics is in agreement with classical physics when the energy differences between quantized levels are very small.

Successes of the Bohr Theory It accounted for the Balmer series and other series.

It predicted a value for the Rydberg constant that agreed strongly with the experimental value.

It gave an expression for the radius of the hydrogen atom.

It predicted the energy levels of hydrogen.

It also works with hydrogen-like (one electron) atoms. Singly ionized helium

It also works with hydrogen-like (one electron) atoms. Doubly ionized lithium

It also works with hydrogen-like (one electron) atoms. Triply ionized beryllium

Four Quantum Numbers The state of an electron is specified by four quantum numbers. These numbers describe all possible electron states. The total number of electrons in a particular energy level is given by:

Principle Quantum Number The principal quantum number (n) where n = 1, 2, 3, … Determines the energy of the allowed states of hydrogen States with the same principal quantum number are said to form a shell K, L, M, … (n = 1, 2, 3, …)

Orbital Quantum Number The orbital quantum number (l) where l ranges from 0 to (n – 1) in integral steps Allows multiple orbits within the same energy level Determines the shape of the orbits States with given values of n and l are called subshells s (l = 0), p (l = 1), d (l = 2), f (l = 3), etc…

Electron Subshells

Generally, the electrons in the s subshell are at the lowest energy level and those in the f subshell in the highest shell occupy the highest energy level.

As the shell number (n) increases the energy difference between the shells diminishes, as shown by the decreasing distance between each successive shell.

Magnetic Quantum Number The magnetic quantum number (ml) where ml ranges from - l to + l in integral steps Explains why strong magnetic fields can cause single spectral lines to split into several closely spaced lines Called the Zeeman effect

Spin Magnetic Quantum Number The spin magnetic quantum number (ms) where ms can only be + 0.5 or – 0.5 Accounts for the fine structure of “single” spectral lines in the absence of a magnetic field

Hydrogen Like Atoms Two important equations for hydrogen-like atoms: Orbital energy Orbital radius

Angular Momentum Physicists agreed that angular momentum was quantized but no one was able to explain why.

Electron Standing Waves de Broglie stated that an electron orbit would be stable if it contained an integral number of electron wavelengths. Analogous to standing waves in a string

Wave Properties It became generally agreed upon that wave properties were involved in the behavior of atomic systems.

Quantum Mechanics And The Hydrogen Atom A review of the various quantum number ranges which are used to determine allowable states n can range from 1 to infinity in integral steps l can range from 0 to (n - 1) in integral steps ml can range from – l to + l in integral steps ms can only be + ½ or – ½

The Spin Magnetic Quantum Number The spin magnetic quantum number explains the splitting of each energy level into two (the Zeeman Effect). It explains how two very closely spaced lines may be formed in the spectra of certain gases. Electron spin (spin-up and spin-down)

Electron Clouds The electron may be found at various distances from the nucleus but the probability of finding it at a distance corresponding to the first Bohr orbit is a maximum. It can be found in a spherical region known as the “electron cloud”.

The Pauli Exclusion Principle Two electrons in an atom can never have the same set of quantum numbers. Because of this, the elements all have different chemical properties. The n = 1 energy level is filled with electrons first.

X-Rays X-rays are emitted when a metal target is bombarded with high-energy electrons to produce: A broad continuous band Bremsstrahlung Characteristic x-rays Kand K

X-Ray Photons What can the incoming electron from an electron gun do to a K-shell electron in a tungsten target atom? It can knock a K-shell electron out of its energy level. Then, an electron from a higher energy level can fall into the K-shell (n = 1). The energy lost by the falling electron shows up as an emitted x-ray photon.

Characteristic X-Rays K-shell emission produces higher-intensity x-rays than Bremsstrahlung. The x-ray photon comes out at a single (characteristic) wavelength. Kor K

Ka X-Rays When an incoming electron forces an electron out of the K shell an electron can drop down from the n = 2 level and a Ka x-ray photon is emitted.

Kb X-Rays When an incoming electron forces an electron out of the K shell an electron can drop down from the n = 3 level and a Kb x-ray photon is emitted.

Which x-ray photon has the highest energy?

Ka X-Ray Wavelengths The wavelength of the emitted Ka x-ray photon is given by:

Electron Shielding One electron in the K shell partially shields the other from the charge of the nucleus. Because of this, we use Zeff = (Z - 1) in the Ka equation.

K X-Ray Wavelengths The wavelength of the emitted K x-ray photon is given by:

Electron Shielding One electron in the K shell and eight electrons in the L shell partially shield the M-shell electrons from the charge of the nucleus. Because of this, we use Zeff = (Z - 9) in the K equation.