Atomic Structure and Electron Behavior

Electrons are arranged around the atom in shells.
Electrons in a particular shell are approximately the same distance from the nucleus.
Each shell has a limited capacity for electrons.
Subsequent shells are farther away from the nucleus, spatially larger implying electrons in outer shells are more distant from the nucleus.

Shells are not physical entities.
Electrons in the same shell move in similar ways, but the exact movement is unknown.
The meaning of 'fitting' electrons into a shell is that only a certain number of electrons can move in the same ways.
Questions to address:
- Why are electrons restricted to move in shells?
- Why is the number of electrons limited in each shell?
- How do electrons move?

It's challenging because atoms are difficult to observe directly.
The uncertainty principle makes it impossible to observe electrons moving around the nucleus.
Spectroscopy is used as an approach.
- Light is shone on a material (atom or molecule).
- The absorbed or emitted light is analyzed.

Light is an oscillating electromagnetic wave with electric and magnetic components.
These components oscillate in time and space.
Waves can be characterized by the distance between peaks, called wavelength ($\lambda$).
Different waves have different wavelengths.
Waves travel at the speed of light (c), a constant.
As a wave travels past a point, the peaks pass with a certain frequency ($\nu$).
The relationship between wavelength and frequency: $\lambda = \frac{c}{\nu}$
- Shorter wavelength corresponds to greater frequency.

The energy of light is crucial because radiation measures the energies of electrons, revealing their movement.
The photoelectric effect is studied to understand this.

Light is shone on a piece of metal.
If the light's properties (frequency, intensity) are appropriate, electrons are ejected (photoelectrons).

Independent variables:
- Frequency of light
- Intensity of light
Dependent variables (measured):
- Electric current (number of photoelectrons)
- Kinetic energy of photoelectrons

Intensity vs. Current:
- As intensity increases, the current increases (more photoelectrons).
- Increasing intensity does not increase the speed of electrons.
Current vs. Frequency:
- No photoelectrons are observed until a threshold frequency ($\nu_0$) is reached.
- Above the threshold, the number of photoelectrons remains constant.
Kinetic Energy vs. Frequency:
- No electrons are observed until the threshold frequency is reached.
- Above the threshold frequency, kinetic energy increases with frequency.

The existence of a minimum threshold frequency is a key characteristic.
Increasing intensity alone cannot cause electron ejection if below the threshold frequency.
Kinetic energy is independent of intensity.
Einstein explained that the photoelectric effect implies that light energy is quantized into packets called photons.

Stream of Water (Garden Hose):
- Increasing intensity might eventually break the glass with a fire hose.
Throwing Objects:
- Ping pong balls (high intensity) will not break the glass.
- Baseballs (low intensity) can break the glass with a single throw.

Low-intensity, high-frequency photons can eject electrons, while high-intensity, low-frequency photons cannot.
Energy is delivered in individual packets.

The kinetic energy of ejected electrons increases proportionally with the frequency of light above the threshold.
The energy of a photon is given by $E = h\nu$ , where:
- $E$ = energy of the photon
- $h$ = Planck's constant
- $\nu$ = frequency of the light
Each photon can eject a single electron.
Increasing intensity increases the number of photons, subsequently increasing the number of photoelectrons.

Energy is quantized into packets (photons).
Each packet (photon) has energy $E = h\nu$ . Photon energy is related to frequency not intensity.

Hydrogen is placed in an electric arc to energize it.
The energized hydrogen emits specific frequencies of radiation.
A prism separates these frequencies for observation.
The visible spectrum of hydrogen consists of four specific frequencies or wavelengths.
Many other frequencies exist outside the visible range.

The Rydberg equation can predict every frequency emitted by hydrogen: $\nu = R \left( \frac{1}{n^2} - \frac{1}{m^2} \right)$ , where
- $\nu$ is the frequency of the emitted light,
- $R$ is the Rydberg constant,
- $n$ and $m$ are integers with m > n .

Atoms emit specific frequencies of radiation.
Frequency of radiation is related to the energy of emitted photons ( $E = h\nu$ ).
Atoms can only lose specific energies.
Only certain energy transitions can occur.
Only specific energy levels exist for electrons within the atom.

The energy of the photon corresponds to the negative of the energy change of the electron: $E<em>{photon} = -\Delta E</em>{electron}$ .
The Rydberg equation can be rewritten in terms of energy levels:
- $\Delta E_{electron} = -hR\left(\frac{1}{n^2} - \frac{1}{m^2}\right)$
This suggests that the energy of the electron is given by:
- $E = -\frac{hR}{n^2}$ , where
  - $E$ is the energy of electron,
  - $h$ is Plank's constant
  - $R$ is Rydberg constant
  - $n$ is an integer corresponding to a quantum number
$n$ is a quantum number that arises naturally from experimental data.

Each element has its own characteristic spectrum.
The Rydberg equation only applies to hydrogen.
Each atom has its own characteristic set of energy levels.
These energy levels can be determined experimentally by measuring the emitted spectrum.