Atomic Theory

Photon Theory

In the early 20th century, scientists came to realize that EMR had wave particle duality

Energy of ONE photon is hf or hc/lambda

This means that high frequency EMR would have the highest energy photons.

The units will be electron volts since photon energies are so small. 1 ev= 1.6×10^-19 J. There are 2 constants that you use for h depending on if the energy is in Joules or eV

Classic physics says brightness is determined by amplitude of EMR (wave theory), quantum physics says it’s determined by the # of photons,

Et= n*Ephoton where n is the NUMBER of photons. This formula assumes the light is MONOCHROMATIC, so all the photons have the same energy.

MORE FREQUENCY MEANS MORE ENERGY in photon theory

Photoelectric effect (PARTICLE PROPERTY ONLY)

Hertz discovered that HIGH FREQUENCY light ejecting electrons produces a photocurrent. He shone a high f light on a cathode and had electrons emitted from its surface and have them converge on the anode

According to wave theory, enough work/energy has to be eject the electrons from the metal. They assumed that bright EMR has more energy, which will eject electrons at a higher rate. This ended up being wrong.

1st Result of Herzl’s experiment

ONLY HIGH FREQUENCY EMR creates photocurrent; the incident EMR must be higher than a metal’s threshold frequency. Einstein called the minimum amount of energy needed to emit the surface electrons W

W=hf_0, where f_0 is the minimum frequency needed to emit the electron

E_photon = W + E_kmax when the frequency is bigger than the minimum frequency and there is some energy left over as kinetic energy

MAKE SURE YOU CONVERT Ek from ev to JOULES

If white light is shone on a metal surface and it asks for the greatest possible speed, you have to use VIOLET LIGHT (400nm) because it has the greatest frequency.

2nd Result of Experiment

Brighter EMR creates more photocurrent; photocurrent has a DIRECT RELATIONSHIP with the intensity of the incident EMR.

Einstein explained that the brighter the incident EMR the more photons that are shone on the metal surface. Each electron absorbs one photon so this leads to more electrons being emitted, creating photocurrent

Frequency determines whether electrons are emitted at all (and their maximum kinetic energy), while intensity affects the current created by emitted electrons after photon absorption (photocurrent), provided the frequency is above the threshold frequency.

Millikan’s Device

Modified a photocell with a back voltage to slow down surface electrons until there is no current (V_stop).

E_kmax= q_eV_stop

q_e is the magnitude of the charge

V_stop is the minimum back voltage required to stop the photocurrent

q_e is the same as 1 eV

E_k= hf-W was Millikan’s experiment in a nutshell. This is in slope intercept form; the x intercept is the minimum frequency and the y int is the magnitude of the Work

Compton effect (PARTICLE PROPERTY ONLY)

Compton shot x-rays through thin carbon foil and saw that many were significantly deflected with a longer wavelength. This is the COMPTON effect. Defied wave theory b/c frequency should never change when it leaves source and there should be no refraction.

This meant the photon was showing momentum properties.

E=pc where E is photon energy and p is momentum

p= h/lambda where h HAS to be the joule constant 6.63×10^-34 J

The Compton equation is the one with the delta lambda. It was derived from conservation of energy and momentum analysis. Remember, ONLY USE THE JOULE CONSTANT OF h FOR THIS ONE.

Basically since energy is inverse to wavelength and the photon gave some of its energy to electrons, the wavelength would increase

When calculating the angle, you have to go WITH THE HORIZONTAL that you hit it with between the deflected xray and the particle it hit

When doing the kinetic energy formula just know that it’s the initial kinetic energy of the xray equal to its final kinetic energy plus the kinetic energy of the other particle. The kinetic energy of the xray is just hc/lambda

If the x-ray is still going one dimension after a collision then the angle is 180. If it goes to another dimension it is 90 degrees.

If you don’t know the missing side of the momentum of a particle, use VECTOR ADDITION AND SOLVE. You can also use this to find the particle’s ANGLE OF DEFLECTION. But if there’s an intermediate direction, you HAVE to use components.

Stop overthinking when it gives you the angle of deflection for the xray after collision. If it tells you x degrees much intermediate direction then just USE THAT.

Models of the Atom Progression

Dalton’s Billiard Ball Model

Atoms are indivisible solid spheres and the smallest possible thing.

Disproved by: Set up a cathode ray tube containing two parallel plates in a glass tube attached to a high voltage source. Observed coloured rays moving from negative to positive plate (cathode rays). NOT EMR because they were deflecting in a magnetic field.

JJ Thomson’s Plum Pudding Model

Atoms have tiny negative particles floating in a dense cloud of positive charge

Disproved by: Rutherford’s gold foil experiment showed 99% of particles moved through but 1% were fully launched back. Positive charge must be in a singular, dense volume (the nucleus).

Rutherford’s Nuclear Model

Atoms is mostly empty space with tiny dense positive nucleus in center and electrons were in orbit around nucleus

Disproved by: An electron should be accelerating and thus losing energy to emit EMR. That would make it spiral into the nucleus

Neils Bohr’s Orbital model

Electrons r restricted to specific quantized energy levels and cannot exist between.

Disproved by: The fact that it could only explain the spectra for hydrogen and not more complex atoms with more than one electron, why certain orbits were allowed, or why the orbiting electrons didn’t produce EMR

Louis de Broglie’s Matter waves

Electrons have like waves. An orbit is only possible if the electrons wavelength fits perfectly in the circle’s circumference as a standing wave. Only certain distances allow the electrons-wave to vibrate w/o destroying itself.

Disproved by: The fact that an electron being small and wave like made it impossible to tell location and speed. So no orbits

Heisenberg and Schrodinger

Heisenberg determined it and Schrodinger did the math for the location. He replaced 2d rings with 3d “clouds of probability”

Cathode ray experiment to get properties of electrons

MUTUALLY PERP FIELDS > ONLY MAGNETIC FIELD > q/m ratio w/ Thomson and Milikan > FOUND MASS OF ELECTRON

Electrons were horizontally fired from cathode ray and deflected using perp electric fields and magnetic fields (parallel plates and coils of wire).

Step 1: Undeflected electrons

Both fields were adjusted so the electron would travel through undeflected

This means the electric force and magnetic force are equal and OPPOSITE

vB= E

Step 2: Deflection in magnetic field

The electric field is turned off and leaves a magnetic field. This leaves a magnetic force

qb= mv/r

This gives us the charge-mass ratio of q/m= v/br

If we coupled this with Milikan’s experiment where he found the elementary charge you can derive the mass.

Atomic Soectra

Continuous Spectra are hot solids, liquids, and dense gases that emit light with a continuous spectrum.

Emission Spectra are heated low pressure GASES that emit certain frequencies of light. It shows discrete bright bands, but mostly dark.

Absorption Spectra occur when white light passes through cold gas, so it shows discrete dark bands, but mostly light.

Homework question where you had to match the identities and there were more than one element on each spectra: CHECK OFF

Bohr Model of Hydrogen

Orbital radii and energies are quantized.

The electrons should have the exact energy to be where they are. When the electron is inside the atom the orbital energy is quantized and the energies r negative. It’s the opposite when it’s outside

Minimum energy to remove an electron from the atom is ionization energy. Formula is based on cons. of energy

Orbital electrons are in uniform motion so (kq²)/r= mv²

To go down an energy level u EMIT PHOTONS to go up u ABSORB PHOTONS

Energy gained or lost (transition energy) must be equal to the photon energy.

Explanation for hydrogen:

Excited hydrogen atoms in cathode rays drop to lower energy levels and emit photons. The range for hydrogen is infrared to ultraviolet in terms of highest to lowest energy lost. A small drop is infrared and a large drop is uv. You can apply the same idea to absorption

3 movements- Blue

4 movements- Violet

5 and up movements- UV

“Unexcited atom” means it’s at GROUND STATE

Quantum mechanics

Electrons formed many lines through two slits which showed evidence of diffraction and interference; wave like properties. If particle theory were true then 2 lines would be formed but multiple were.

Misconceptions/Mistakes

The kinetic energy that an electron hits an unexcited atom is the amount of energy that it LOSES. You should get the initial kinetic energy already and subtract how much you lost from that to find the final.

If you want to know how many transitions make visible light, REMEMBER THE 700-400nm range

Power is n times energy of photon divided by s

COMPTON EQUATION MEASURES ENERGY AND MOMENTUM, Photoelectri effect JUST energy. my