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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

    Example of a half-life graph

    • 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

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

    Example of a half-life graph

    • 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