Atomic Theory

Photoelectric effect

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

1st Result of Herzl’s experiment

Only high f ENR 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

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

current

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

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 balanced

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.

Cathode ray experiment to get properties of electrons

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 balanced

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.

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.

Orbital electrons are in uniform motion so F_e=F_c

To go down an energy levels u emit photons to go up u absorb

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. So the drop to n=1 would be uv and the drop to n=3,4,5 etc would be infrared since it’s a small drop. Absorption is simply the reverse.

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.