Chapter 7 - Quantum, Atomic, and Nuclear Physics

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)

Applications: solar panels, photosynthesis, tanning, photographic film

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

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

representing the probability of finding the particle at a specific location**wave function**Ѱ: wave function

Ѱ = 0: no probability of finding the graph

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

Particles involved with nuclear decay:

: two protons and two neutrons together (helium nucleus)**Alpha particle (𝞪)**: either an electron or positron**Beta particle (β)**): a gamma ray photon - massless and chargeless**Gamma particle (Ɣ**

__Isotopes__- same atomic number of an element but different mass numbersNotation 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 emittedβ+ (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 photonThe photon carries away some energy and momentum so the nucleus recoils

__Neutron deca__y: a neutron is emitted

: the slight difference in mass between the total mass present before the decay and after the decay**Mass defect**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 amountLonger half life → slow decay rate

__Fission reactions__: when a heavy nucleus is split into two chunksBegun 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

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)

Applications: solar panels, photosynthesis, tanning, photographic film

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

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

representing the probability of finding the particle at a specific location**wave function**Ѱ: wave function

Ѱ = 0: no probability of finding the graph

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

Particles involved with nuclear decay:

: two protons and two neutrons together (helium nucleus)**Alpha particle (𝞪)**: either an electron or positron**Beta particle (β)**): a gamma ray photon - massless and chargeless**Gamma particle (Ɣ**

__Isotopes__- same atomic number of an element but different mass numbersNotation 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 emittedβ+ (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 photonThe photon carries away some energy and momentum so the nucleus recoils

__Neutron deca__y: a neutron is emitted

: the slight difference in mass between the total mass present before the decay and after the decay**Mass defect**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 amountLonger half life → slow decay rate

__Fission reactions__: when a heavy nucleus is split into two chunksBegun 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