# Chapter 7 - Quantum, Atomic, and Nuclear Physics

## Basics

• Einstein’s postulates of special relativity

• All laws of physics remain the same in a uniformly moving frame of reference

• The speed of light in a vacuum is always 3 x 10^8 no matter the motion of the source of light or the observer

• Summary: time and distance are relative according to your frame of reference

• E = mc^2

• Mass is a solid form of energy and can be converted into energy and vice versa

• Big 4 subatomic particles

• Proton (p)

• Mass = 1.67 x 10^-27 kg = 1 amu

• Charge: positive

• Electron (e)

• Mass = 9.11 x 10^-31 kg

• Charge: negative

• Neutron (n)

• Mass = 1.67 x 10^-27 kg = 1 amu

• Charge: 0

• Photon (ɣ)

• Mass = 0

• Charge: 0

• Electron-Volts (eV)

• Electron-Volt: a unit of energy - the amount of energy needed to change the potential of an electron by 1 volt

• 1 eV = 1.6 x 10^-17 J

• Photons

• Light is made of photons

• E = hf = hc/λ

• E: energy of a photon

• h: Planck’s constant = 6.63 x 10^-34 Js = 4.14 x 10^-15 eVs

• f: frequency (Hz)

• c: speed of light (3 x 10^8 m/s)

• λ: wavelength (m)

## Photoelectric Effect

• Applications: solar panels, photosynthesis, tanning, photographic film

• Photoelectric effect: when incident light is shined on a metal, electrons detach

• K(max) = hf - ɸ

• K(max): max kinetic energy of the emitted electron

• h: Planck’s constant

• f: frequency

• hf: energy of the incident photon

• ɸ: work function - the energy required to remove an electron from a specific element/material

• When the frequency of incident light increases, the maximum kinetic energy of the emitted electron increases linearly

• Threshold frequency: minimum frequency for electron emission

• Photon Momentum

• When a photon collides with an atom and the atom emits an electron, momentum and energy are conserved

• p = h/λ = E/c

## DeBroglie Wavelength

• If a particle has a shorter wavelength, it behaves more like a particle

• If a particle has a longer wavelength, it behaves more like a wave

• To find the wavelength for a particle (de Broglie’s wavelength), use λ = h/p = h/mv

• λ: de Broglie’s wavelength

• p: momentum of particle

• Particles have a wave function representing the probability of finding the particle at a specific location

• Ѱ: wave function

• Ѱ = 0: no probability of finding the graph

## Energy Levels in an atom

• For an electron to move from one energy level to another, it will either have to absorb or emit energy in the form of a photon

• The nucleus of an atom is positive and electrons are negative so it takes energy to pull the electron away from the nucleus by overcoming their attractive force

• Electrons take less energy if they’re in a higher energy level

• Key points

• n1 is called the ground state - the lowest possible energy level for the electron

• Moving from lower to higher energy levels tells you the atom absorbed a photon

• Moving from higher to lower energy levels tells you the atom emitted a photon

• There are no intermediate levels between energy levels

• E (photon) = E (final) - E (initial)

• If there is extra energy after jumping from one energy level to another, that energy is converted to kinetic energy of the emitted electron

## Nuclear Decay

• Particles involved with nuclear decay:

• Alpha particle (𝞪): two protons and two neutrons together (helium nucleus)

• Beta particle (β): either an electron or positron

• Gamma particle (Ɣ): a gamma ray photon - massless and chargeless

• Isotopes - same atomic number of an element but different mass numbers

• Notation for Isotopes: element symbol with two small numbers to the left (one on top of the other)

• Top number on the left side of the symbol: mass number = neutron # + proton #

• Bottom number on the left side of the symbol: # of protons in the nucleus = atomic number

• Alpha (𝞪) decay: a Helium nucleus is emitted from the original isotope

• Beta (β) decay: either a positron or electron is emitted

• β+ (also symbolized as e+): positron - +1 charge with negligible mass

• β- (also symbolized as e-): electron - -1 charge with negligible mass

• Gamma (Ɣ) decay: massless and chargeless photon

• The photon carries away some energy and momentum so the nucleus recoils

• __Neutron deca__y: a neutron is emitted

• Mass defect: the slight difference in mass between the total mass present before the decay and after the decay

• This difference in mass is destroyed and converted into kinetic energy

• E = Δmc^2

• Δm: mass defect

• c: speed of light

• E: energy produced

• 1 u = 931 MeV/c^2

• The mass defect may become the nuclear binding energy and will be equal to the strong nuclear force that holds the nucleus together

• Half-life: the time it takes for a radioactive isotope to decay half its original amount

• Longer half life → slow decay rate

• Fission reactions: when a heavy nucleus is split into two chunks

• Begun by shooting a neutron into the nucleus

• Nuclear power plants and weapons

• Fusion reactions: when two light nuclei combine to make a heavier and stable nucleus

• Induced Reaction: scientists bombard a nucleus with high-speed particles to induce the emittance of a proton

• Antimatter: every normal particle has an antimatter to match it (electron and positron)

• When matter and antimatter meet, they annihilate each other

• Ex: electron and positron can turn into photon energy

• E (electron) + E(positron) = (2m)c^2 = hf

• m: mass of electron

• c: speed of light

• h: Planck’s constant

• f: frequency