10. Quantum and Nuclear Physics

Atomic Nucleus

Dense core of protons and neutrons surrounded by electron cloud

4 fundamental forces:

1. Gravitational

2. Electromagnetism

3. Strong nuclear forces

4. Weak nuclear forces

Strong Nuclear Force

Interactions between protons and neutrons that keep protons together (stronger than electromagnetic forces)

Nuclear Binding Energy

Potential energy found in every nucleus that holds protons together despite repulsions

E =

mc²

Mass-energy Equivalence

Proposed by Einstein, resulting in equation E = mc²

Mass defect

Difference between experimental and calculated atomic masses due to binding energy1

1 eV

Energy equivalent to work needed to move an electron through voltage of 1V

1 eV =

1.602 × 10^-19 J

Bohr Model of the Atom

Obsolete theory that suggested electrons orbit nucleus in one of limited number of stable orbital levels

Unique Property of Electrons

Show wave and particle duality like light does

De Broglie Equation

λ = h/mv

Orbitals

The areas which a probability wave is dispersed for an electron

Pauli Exclusion Principle

No two electrons in an atom can have the same set of quantum numbers

Heisenberg Uncertainty Principle

We can establish the position of a particle and its momentum to a certain degree of uncertainty

Photoelectric Effect

Substance emits electrons in response to photons being shined onto it due to exciting the electrons

When electrons are ejected…

The electron becomes proportional to the intensity of light

Insights to Photoelectric Effect

1. Enough energy must be provided to eject electrons

2. Energy is dependent on the frequency of light

E_photon =

hf = hc/λ

Work Function

E_{work function} = hf_threshold

What is work function?

The minimum amount of energy needed to eject an electron

What happens is photon carries more energy than needed?

The excess energy not going towards work function is kinetic energy

KE_max =

E_incident - E_{work function} = hf_incident - hf_{work function}

Rydberg Equation

1/λ = R_H(1/n₁² - 1/n₂²) using R_H = 1 × 10^-7 m^-1

E = R_H(1/n₁² - 1/n₂²) using R_H = 2.18 × 10^-18 J

Emission Spectra

Black background on which emitted wavelengths appear in color

Absorption Spectra

Colored background with black lines for wavelengths absorbed

On a graph, low absorbance means…

More light is being reflected back (and likely showing color)

Atomic Number

Number of protons that an atom has

Atomic Weight

Protons and neutrons added together

isotopes

Different forms of an element by varying the number of neutrons

2 types of nuclear reactions:

1. Nuclear fission

2. Nuclear fusion

Nuclear Fusion Example

Helium production by the sun via fission of deuterium and tritium

²₁H + ³₁H → ⁴₂He + ¹₀n + energy

Nuclear Fission

Neutron collides with an atom, breaking the nucleus of the atom down into two other atoms

Radioactive Decay

Spontaneous breakdown of isotopes which eject mass as radiation

Types of Radioactive Decay

1. Alpha

2. Beta

3. Gamma

More massive particles…

Are more dangerous and more shielded against

Alpha Decay

Alpha particle (Helium nucleus) is emitted

Alpha particle

Helium nuclei with 2 protons, 2 neutrons, and 2+ charge

Very dangerous but easily shielded

Beta Decay

Beta particle is emitted, two main types (- and +)

Beta-minus Decay

Neutron is converted into a proton, causing an electron to eject

Beta-plus Decay

A neutron is converted into an electron, and a proton is ejected

Move left on periodic table

Beta particles

Less massive, so less dangerous but harder to shield

Gamma Decay

Gamma rays have no mass or charge, so c just represents energy lost

Gamma Rays

Very penetrable and can have health-risks but less than beta and alpha

Electron Capture

Not technically decay; nucleus grabs electron changing a proton into a neutron (charges cancel)

Move left on periodic table

Half Life

Time it takes for half of a radioactive sample to decay (t_1/2)

t_1/2 =

.693/λ

Graph of Radioactive Decay

` BUT can be displayed as semi-log which shows a linear relationship

Applications of Radioactive Decay

PET scans detect where radioactive particles are emitted to make images

Radiolabeling

Incorporating radioactive atom to trace flow of atoms