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Nuclear Physics

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Quantum Physics Physics on a very small (e.g., atomic) scale is “quantized”. Quantized phenomena are discontinuous and discrete, and generally very small. Quantized energy can be thought of as existing in packets of energy of specific size. Atoms can absorb and emit quanta of energy, but the energy intervals are very tiny, and not all energy levels are “allowed” for a given atom.

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Light: Ray We know from geometric optics that light behaves as a ray. This means it travels in a straight line. When we study ray optics, we ignore the nature of light, and focus on how it behaves when it hits a boundary and reflects or refracts at that boundary.

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Light: Wave We will frequently use one equation from wave optics in quantum optics. c = λf c: 3 x 10 8 m/s (the speed of light in a vacuum) λ: wavelength (m) (distance from crest to crest) f: frequency (Hz or s -1 )

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Light: Particle Light has a dual nature. In addition to behaving as a wave, it also behaves like a particle. It has energy and momentum, just like particles do. Particle behavior is pronounced on a very small level, or at very high light energies. A particle of light is called a “photon”.

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Photon Energy The energy of a photon is calculated from it the frequency of the light. E = hf E: energy (J or eV) h: Planck’s constant 6.625×10 -34 J s 4.14 ×10 -15 eV s f: frequency of light (s-1, Hz)

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Check Which has more energy in its photons, a very bright, powerful red laser or a small key-ring red laser? Which has more energy in its photons, a red laser or a green laser?

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Electron Volts The electron-volt is the most useful unit on the atomic level. If a moving electron is stopped by 1 V of electric potential, we say it has 1 electron-volt (or 1 eV) of kinetic energy. 1 eV = 1.602×10 -19 J

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Problem What is the frequency and wavelength of a photon whose energy is 4.0 x 10 -19 J?

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Problem How many photons are emitted per second by a He-Ne laser that emits 3.0 mW of power at a wavelength of 632.8 nm?

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Atomic Transitions

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Energy Levels This graph shows allowed quantized energy levels in a hypothetical atom. The more stable states are those in which the atom has lower energy. The more negative the state, the more stable the atom.

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Energy Levels The highest allowed energy is 0.0 eV. Above this level, the atom loses its electron. This level is called the ionization level. The lowest allowed energy is called the ground state. This is where the atom is most stable. States between the highest and lowest state are called excited states.

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Energy Levels Transitions of the electron within the atom must occur from one allowed energy level to another. The electron CANNOT EXIST between energy levels.

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Photon Absorption When a photon of light is absorbed by an atom, it causes an increase in the energy of the atom. The photon disappears. The energy of the atom increases by exactly the amount of energy contained in the photon. The photon can be absorbed ONLY if it can produce an “allowed” energy increase in the atom.

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Photon Absorption When a photon is absorbed, it excites the atom to higher quantum energy state. The increase in energy of the atom is given by ΔE = hf. -10eV 0eV

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Absorption Spectra When an atom absorbs photons, it removes the photons from the white light striking the atom, resulting in dark bands in the spectrum. Therefore, a spectrum with dark bands in it is called an absorption spectrum.

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Absorption Spectra Absorption spectra always involve atoms going up in energy level. -10eV 0eV

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Photon Emission When a photon of light is emitted by an atom, it causes a decrease in the energy of the atom. A photon of light is created. The energy of the atom decreases by exactly the amount of energy contained in the photon that is emitted. The photon can be emitted ONLY if it can produce an “allowed” energy decrease in an excited atom.

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Photon Emission When a photon is emitted from an atom, the atom drops to lower quantum energy state. The drop in energy can be computed by ΔE = hf. -10eV 0eV

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Emission Spectra When an atom emits photons, it glows! The photons cause bright lines of light in a spectrum. Therefore, a spectrum with bright bands in it is called an emission spectrum.

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Emission Spectra Emission spectra always involve atoms going down in energy level. -10eV 0eV

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Problem What is the frequency and wavelength of the light that will cause the atom shown to transition from the ground state to the first excited state? Draw the transition.

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Problem What is the longest wavelength of light that when absorbed will cause the atom shown to ionize from the ground state? Draw the transition.

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Problem The atom shown is in the second excited state. What frequencies of light are seen in its emission spectrum? Draw the transitions.

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The Photoelectric Effect

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Absorption We’ve seen that if you shine light on atoms, they can absorb photons and increase in energy. The transition shown is the absorption of an 8.0 eV photon by this atom. You can use Planck’s equation to calculate the frequency and wavelength of this photon.

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Extra Energy Now, suppose a photon with TOO MUCH ENERGY encounters an atom? If the atom is “photo-active”, a very interesting and useful phenomenon can occur… This is called the Photoelectric Effect.

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Photoelectric Effect Some “photoactive” metals can absorb photons that not only ionize the metal, but give the electron enough kinetic energy to escape from the atom and travel away from it. The electrons that escape are often called “photoelectrons”. The binding energy or “work function” is the energy necessary to promote the electron to the ionization level. The kinetic energy of the electron is the extra energy provided by the photon.

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Photoelectric Effect Photon Energy = Work Function + Kinetic Energy hf = Ф + K max K max = hf – Ф K max : Kinetic energy of “photoelectrons” hf: energy of the photon Ф : binding energy or “work function” of the metal.

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Problem Suppose the maximum wavelength a photon can have and still eject an electron from a metal is 340 nm. What is the work function of the metal surface?

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Photoelectric Effect Suppose you collect K max and frequency data for a metal at several different frequencies. You then graph K max for photoelectrons on y- axis and frequency on x-axis. What information can you get from the slope and intercept of your data?

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The Photoelectric Effect The Photoelectric Effect experiment is one of the most famous experiments in modern physics. The experiment is based on measuring the frequencies of light shining on a metal (which is controlled by the scientist), and measuring the resulting energy of the photoelectrons produced by seeing how much voltage is needed to stop them. Albert Einstein won the Nobel Prize by explaining the results.

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Photoelectric Effect Diagram

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Photoelectric Effect Voltage necessary to stop electrons is independent of intensity (brightness) of light. It depends only on the light’s frequency (or color). Photoelectrons are not released below a certain frequency, regardless of intensity of light. The release of photoelectrons is instantaneous, even in very feeble light, provided the frequency is above the cutoff.

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Photoelectric Effect The kinetic energy of photoelectrons can be determined from the voltage (stopping potential) necessary to stop the electron. If it takes 6.5 Volts to stop the electron, it has 6.5 eV of kinetic energy.

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Momentum

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Mass of a Photon Photons do not have “rest mass”. They must travel at the speed of light, and nothing can travel at the speed of light unless its mass is zero. A photon has a fixed amount of energy (E = hf). We can calculate how much mass would have to be destroyed to create a photon (E=mc 2 ).

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Problem Calculate the mass that must be destroyed to create a photon of 340nm light.

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Photon Momenum Photons do not have “rest mass”, yet they have momentum! This momentum is evident in that, given a large number of photons, they create a pressure. A photon’s momentum is calculated by

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Proof of Photon Momentum Compton scattering Proof that photons have momentum. High-energy photons collided with electrons exhibit conservation of momentum. Work Compton problems just like other conservation of momentum problems except the momentum of a photon uses a different equation.

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Problem What is the momentum of photons that have a wavelength of 620 nm?

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Problem What is the frequency of a photon that has the same momentum as an electron with speed 1200 m/s?

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Matter Waves

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Waves act like particles sometimes and particles act like waves sometimes. This is most easily observed for very energetic photons (gamma or x-Ray) or very tiny particles (elections or nucleons)

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Energy A moving particle has kinetic energy E = K = ½ mv 2 A particle has most of its energy locked up in its mass. E = mc 2 A photon’s energy is calculated using its frequency E = hf

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Momentum For a particle that is moving p = mv For a photon p = h/λ Units?

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Wavelength For a photon λ = c/f For a particle, which has an actual mass, this equation still works λ = h/p where p = mv This is referred to as the deBroglie wavelength

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Matter Wave Proof Davisson-Germer Experiment Verified that electrons have wave properties by proving that they diffract. Electrons were “shone” on a nickel surface and acted like light by diffraction and interference.

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Problem What is the wavelength of a 2,200 kg elephant running at 1.2 m/s?

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Nuclear Decay

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Notation Atomic Mass (Protons + Neutrons) Atomic Number (Protons) Element

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Isotopes Isotopes have the same atomic number and different atomic mass. Isotopes have similar or identical chemistry. Isotopes have different nuclear behavior.

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Half Life The time required for one-half of an element’s to decay.

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Nuclear Particles Proton Charge: +e Mass: 1.66 x 10 -27 kg (1 amu) Neutron Charge: 0 Mass: 1.66 x 10 -27 kg (1 amu) Electron Charge: -e Mass: 9.1 x 10 -31 kg (1/2000 amu)

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Decay Nuclear Decay: a spontaneous process in which an unstable nucleus ejects a particle and changes to another nucleus. Alpha decay Beta decay Beta Minus Positron Fission: a nucleus splits into two fragments of roughly equal size. Fusion: Two nuclei combine to form another nucleus.

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Decay Alpha decay A nucleus ejects an alpha particle, which is just a helium nucleus. Beta decay A nucleus ejects a negative electron. Positron decay A nucleus ejects a positive electron.

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Alpha Decay Alpha particle (helium nucleus) is released. Alpha decay only occurs with very heavy elements.

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Beta Decay Beta decay occurs when a nucleus has too many neutrons for the protons present. A neutron converts to a proton. An antineutrino is also released.

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Neutrinos Proposed to make beta and positron decay obey conservation of energy. These particles possess energy and spin, but do not possess mass or charge. They do not react easily with matter and are extremely hard to detect.

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Gamma Radiation Gamma photons are released by atoms which have just undergone a nuclear reaction when the excited new nucleus drops to its ground state. The high energy in a gamma photon is calculated by E = hf.

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Energy in Nuclear Reaction

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Mass Energy Matter is created from energy and can be converted into energy through nuclear reactions. E = mc 2 E – Energy (J) M – mass (kg) c – speed of light (3x10 8 m/s)

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Energy in Nuclear Reactions 1.Add up the mass (in atomic mass units, u) of the reactants. 2.Add up the mass (in atomic mass units, u) of the products. 3.Find the difference between reactant and product mass. The missing mass has been converted to energy. 4.Convert mass to kg ( 1 u = 1.66 x 10 -27 kg) 5.Use E = mc 2 to calculate energy released.

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Problem Complete the reaction, identify the type of decay, and calculate the energy.

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Fission Fission occurs when an unstable heavy nucleus splits apart into two lighter nuclei, forming two new elements. Fission can be induced by free neutrons. Mass is destroyed and energy produced according to E = mc 2.

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Fusion Fusion occurs when two light nuclei come together to form a new nucleus of a new element. Fusion is the most energetic of all nuclear reactions. Energy is produced by fusion in the sun. Fusion of light elements can result in non- radioactive waste.

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