The Evolution of the Atomic Model:Thomson’s plum-puddingRutherford’s nuclear model

An electron in orbit about the nucleus must be accelerating; an accelerating electron give off electromagnetic radiation. So, an electron should lose energy and spiral into the nucleus.

Gases in sealed tubes can be made to emit electromagnetic radiation with a potential difference. The light emitted can be split into wavelengths by a spectroscope.

The result is a series of bright lines or fringes called a line spectrum. Similar series of spectra have been found in the invisible spectrum, at both shorter and longer wavelengths than the visible.

The group in the visible region is called the Balmer series. The Lyman series is comprised of waveleghts shorter than the visible spectrum; and the Paschen series of longer wavelengths than the visible.

Empirical equations:

Lyman series:1/λ = R(1/12 - 1/n2) n = 2,3,4,...Balmer series:1/ λ = R(1/22 - 1/n2) n = 3,4,5,...Paschen series:1/ λ = R(1/32 - 1/n2) n = 4,5,6,...

R is the Rydberg constant, R = 1.097 x 107 m-1.

Ex 2 - Find (a) the longest and (b) the shortest wavelengths of the Balmer series.

The equations show where the lines are found, but they do not explain why.

Neils Bohr’s model of the atom explains the why. Bohr hypothesized that there are only certain values for the total energy (kinetic energy plus potential energy) of an orbiting electron.

These energy levels correspond to different electron orbits. Bohr also assumed that in these orbits an electron does not radiate electromagnetic energy. They are called stationary orbits or stationary states.

Bohr knew that radiationless orbits violated the laws of physics, but he knew they must exist. He utilized Einstein’s photon concept by theorizing that a photon is emitted only when an electron moves from a higher energy orbit to a lower energy one.

Electrons get to the higher energy level when they pick up energy as atoms collide. This occurs more often when atoms are heated up or stimulated by a flow of electricity.

When an electron moves to a lower energy level, the energy of the photon is Ei - Ef. A photon’s energy is hf, so Ei - Ef = hf. Bohr used this equation to find λ.

The formula for the radii of the Bohr orbits in meters is: rn = (5.29 x 10-11)n2/Zn is the orbit number,Z is the number of protons.

If Z = 1 and n = 1, it is the smallest Bohr orbit of a hydrogen atom: 5.29 x 10-11 m.

This the Bohr radius.

The Bohr energy levels in joules:En = -(2.18 x 10-18 J)Z2/n2

n is the orbit number,Z is the number of protons.

The Bohr energy levels in electron volts:(1.6 x 10-19 J = 1 eV)En = -(13.6 eV)Z2/n2

n is the orbit number,Z is the number of protons.

Ex 3 - Find the ionization energy that is needed to remove the remaining electron from Li2+.

Bohr’s calculations led to a calculation of the Rydberg constant. Bohr’s theory’s major accomplishment was the agreement between the theoretical and experimental values of the Rydberg constant.

The Lyman series is produced when an electron’s transition is from higher levels to the first level. In the Balmer series, electrons end up in level two. Electrons reach level three from higher levels in the Paschen series.

There is a different amount of energy released in each case, so the frequency and wavelength of the photon emitted is different in each case.

When electrons move to lower energy levels, photons are emitted, so these are called emission lines.

If light with a range of wavelengths passes through a gas, some photons are absorbed as they excite electrons to a higher energy level.

These are called absorption lines, which appear as gaps in the continuous spectrum.

Bohr’s equation for the angular momentum of the electron was:Ln = mvnrn = nh/2π.n = 1,2,3,...

de Broglie pointed out that the electron in its circular orbit must be pictured as a particle wave.

As with any wave, resonance can form a standing wave when the distance traveled is any integer number of wavelengths.

The total distance around a Bohr orbit of radius r is the circumference or 2πr. The condition for a standing particle wave would be 2πr = nλ. n = 1,2,3,... “n” is the number of whole wavelengths that fit into the circumference of the circle.

In a particle wave, the de Broglie wavelength of the electron is λ = h/p (p is the electron’s momentum and is equal to mv). 2πr = nλ becomes 2πr = nh/mv. Rearranged, this is mvr = nh/2π. n = 1,2,3,... This is what Bohr assumed for the angular momentum of the electron.

De Broglie’s explanation emphasizes the fact that particle waves play an important role in the structure of the atom.

While Bohr’s model uses a single quantum number, quantum mechanics reveals that four different quantum numbers are needed to describe each state of the hydrogen atom.

1. The principle quantum number n. Total energy of the electron, n = 1,2,3,...

2. The orbital quantum number l. Angular momentum of the electron, l = 0,1,2,...(n-1) andL = √l(l+1)•h/2π

3. The magnetic quantum number ml. An external magnetic field influences the energy of the atom.

ml = -l,...,-2,-1,0,1,2,...,+land angular momentum in the z direction is Lz = ml h/2π

4. The spin quantum number ms. Describes the electron’ s spin angular momentum.

ms = +1/2 or ms = -1/2

As the principle quantum number n increases, the number of possible combinations of the four quantum numbers (and therefore, the number of possible states of the atom) increases rapidly.

Ex 5 - Determine the number of possible states for the hydrogen atom when the principle quantum number is (a) n = 1 and (b) n = 2.

While the Bohr model predicts an exact orbit for the electron, in reality this is just the most probable location of the electron. Actually it is found somewhere in an electron cloud around the nucleus.

This cloud takes different, more complex shapes than spherical as the possible values of the orbital quantum number increase.

The Bohr model predicts a specific location for an electron’s orbit. From this we can calculate a specific velocity. This means a specific momentum. But remember, the Heisenberg uncertainty principle states that specific location and specific momentum can’t both be known.

When calculated, the possible locations of the electron in hydrogen range from r = 0 to twice the Bohr radius! The Bohr model, while useful, does not represent the reality of the atom.

In multiple-electron atoms, electrons with the same value of n are said to be in the same shell.n = 1, the K shelln = 2, the L shelln = 3, the M shell

If the electrons have the same value of n and l, they are in the same subshell. The n = 1 shell has a single l = 0 subshell. The n = 2 has two subshells: l = 0 and l = 1. If n = 3, three subshells: l = 0, l = 2, l = 3.

When at room temperature, an atom’s electrons spend most of their time in the lowest energy levels possible. This lowest-energy state is called the ground state.

However, when a multiple-electron atom is in its ground state, not every electron is in the n = 1 shell. The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of values for the four quantum numbers: n, l, ml, and ms.

Ex 8 - Determine which of the energy levels are occupied by electrons in the ground state of hydrogen, helium, lithium, beryllium, and boron.

The l = 0 subshell, s The l = 1 subshell, pThe l = 2 subshell, dThe l = 3 subshell, fThe l = 4 subshell, gThe l = 5 subshell, h

A shorthand notation used is as follows:

2p5

2 in this case is n,p is l,5 is the number of electrons in the subshell

This subshell filling explains the orientation of the periodic table. In the transition metals 3d, 4d, 5d, and 6d are filled; lanthinide: 5d and 4f; actinide: 5f and 6d.

LightAmplification byStimulatedEmission ofRadiation

Single frequency-monochromaticConstant phase relationship

Light flash into a ruby crystal sends photons into the crystal. This sends some atoms into a higher energy state, electrons drop into lower energy levels releasing more photons.

These photons excite more atoms, etc. This results in an amplification of the photon beam.

Since the crystal is of a specific length, a standing wave of single-frequency light is produced. As intensity increases, photons pass through a partially reflective end in intense pulses of coherent red light.