# Particle Nature of Light

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Particle Nature of Light
In the 19th century, James Clerk Maxwell proposed that light acted like a wave made up of two fields: An electric field caused by stationary electric charges A magnetic field caused by moving electric charges 1831 – 1879 Scottish Physicist and Mathematician It was understood that charged particles move in an object causing it to give off electromagnetic radiation (in the form of heat or light)..

In the 20th century, Albert Einstein and Max Planck rethought the whole idea of light.
Instead of thinking of light as being a wave, Einstein thought of it as an energized particle called a “photon” In this theory, when something gives off light, it is releasing photons. German Physicist

Einstein believed that the amount of energy in the photons was proportional to the frequency of light produced Example: Yellow light has a frequency of 5.25 x 1014 Hz. What is the energy of the photons? E = hf or E = hc/λ E = energy of single photon (J) h = Planck’s constant (6.63 x Js) F = frequency (Hz) C = speed of light (3 x 108 m/s) λ = wavelength Answer: The photons of yellow light have an energy of 3.48 x J or 2.18 eV 1 eV (electron volt) = 1.60 x J

Max Planck took Einstein’s theory a step further
Max Planck took Einstein’s theory a step further. He theorized that the energy of photons cannot exist in any amount. Photons have discrete amounts of energy called “quanta.” E = nhf or E = nhc/λ n = number of photons Translation: Other energies of yellow light have to be in multiples of 3.48 x J. If you have light with 6.96 x J of energy, that would consist of 2 photons of light. German Physicist

According to Einstein, these photons not only have energy, but they have momentum.
This is true even though photons have no mass. The same laws of motion (and definition of momentum) do not apply to things moving at the speed of light. p = E / c or p = h / λ p = momentum (kgm/s) E = energy (J) c = speed of light h = Planck’s constant λ = wavelength (m)

About 0.1 eV is required to break a “hydrogen bond” in a protein molecule. What is the minimum frequency and maximum wavelength of a photon that can accomplish this? Suppose that 1 x 1019 photons are emitted every 0.25 s from a light bulb that gives off light with a wavelength of 500 nm. What is the momentum of one photon? If all of the light was focused on a piece of black paper and absorbed, what would be the force on the paper?

Photoelectric Effect Albert Einstein discovered that when photons are cast on a metal, they dislodge the electrons in the metal allowing them to leave the surface. This phenomenon is called the photoelectric effect. A photocell is an evacuated glass chamber with a negative metal plate on one side a positively charged cathode on the other When the photocell has a voltage applied to it, electrons flow to the plate and build up. As light is directed on the plate, electrons dislodge and move to the cathode across the gap.

Wave Theory Predictions
From a wave theory perspective, the ejected electrons can be explained by the electric field of the incoming light. The electric field exerts a force on the electrons ejecting them from the metal with a certain kinetic energy. Wave Theory Predictions If the light intensity is increased (greater amplitude), the number of electrons ejected and their kinetic energies should increase because of the greater electric field present. The frequency of light (color) should NOT effect the kinetic energy.

Einstein’s experiments did NOT support these predictions.
Einstein’s Observations More intense light dislodged more electrons, but those electrons did not have more kinetic energy. They traveled at the same speed as those with less intense light. Different frequencies of light caused the dislodged electrons to move with more kinetic energy. Einstein’s Explanation More intense light contains more photons, but the photons have the same amount of energy (discrete quantum level of energy) Changing the frequency changes the amount of energy (E = hf)

For every photon that hits the metal, an electron is dislodged and all the energy is transferred to the electron. The photon ceases to exist. Since electrons are held in the atom by attractive forces, a certain amount of energy is needed just to get the electron to move through the metal. This amount of energy is called the work function (W). Whatever energy is left over changes to kinetic energy causing the electron to move away from the metal at a given speed

hf = KE + W Since the amount of energy given off by the photon is
E = hf hf = KE + W h = Planck’s Constant (6.63 x Js) KE = kinetic energy (J) W = work function (J) There is a threshold frequency (fo) that must be attained in order for the effect to occur. If it is not met, electrons will not move out of the metal across the gap. hfo = W As the frequency of light increases, the speed at which the electrons move increases.

To find out the kinetic energy of the emitted electrons, the voltage of the circuit can be reversed making point C negative. That negative terminal will slow down the emitted electrons. Whatever voltage causes the emitted electrons to stop is called the stopping voltage (V0). We know ∆V = ∆PE/q = ∆KE/q So KE = qV0 KE = kinetic energy of electrons (J) V0 = stopping voltage (V) q = charge of electron (C)

Photocells are used to create electricity in solar panels
Photocells are used to create electricity in solar panels. Incident sunlight creates electric current. Drawback of solar electricity is that it cannot be stored with great efficiency. Also used as switches so that street lights turn on when it gets dark. Circuit Diagram

What is the kinetic energy and the speed of an electron ejected from a sodium surface whose work function is W0 = 2.28 eV when illuminated by light of wavelength of 410 nm? What would be the stopping voltage of the above photocell with the corresponding incident light?

energy is constant value in that orbit
How Photons are Created In the early 20th century, Niels Bohr proposed a new theory about the atom that stated: A single electron moves around the nucleus in a circular orbit known as the ground state Danish chemist and physicist energy is constant value in that orbit

energy is constant value in that orbit
Electrons move in orbits because they have inertia due to their attraction to other atoms along with centripetal attraction toward center because of the positive charge in the nucleus The energy of the electron is quantized, meaning it is restricted to a distinct, constant value energy is constant value in that orbit

When an atom absorbs energy from an outside source (electric current, heat), it can move to an orbit with a higher energy called an excited state. higher E n = 1 lower E n = 2 current Each orbit has a distinct quantum number (n) and a distinct amount of energy (E). Both values increase as you move away from the nucleus.

n = 1 n = 2 higher E lower E current
Upon arriving, it immediately returns to the ground state and releases that same amount of energy in the form of a photon.

Bohr maintained that every energy level had a distinct amount of energy.
For hydrogen, the energy level can be calculated using the formula to the right En = -13.6(1 / n2) En = energy of specific level (electron volts) n = quantum number He also found that the energies of other atoms could be found by modifying the formula to En = -13.6(Z2/ n2) Z = atomic number of atom

The values are negative because E = 0 is typically defined at a point located at infinity. At this point, no energy is needed to remove the electron. The energy of the ground state expressed as a positive number tells you the ionization energy (the energy needed to remove an electron)

The energy of an emitted photon is equal to the difference in the energy levels that the electron traveled between. Eu – El = hf Eu = Energy of upper level (eV) El = energy of lower level (eV) hf = E = energy of photon (eV)

Like all energy, the point that you call E = 0 is a matter of convention.
Typically, lower energy levels are given negative values. Sometimes, the ground state is defined as E = 0 and higher energy levels would have larger values in the positive direction

Since every atom has a unique structure, their electrons behave differently when energized.
Sometimes electrons absorb energy and skip levels Sometimes electrons release energy level by level These different examples of emission are what cause different substances to have different diffraction spectral.

Energy-level diagram for hydrogen
Corresponding spectral series for hydrogen

Determine the wavelength of light emitted when a hydrogen atom makes a transition from the n = 6 to the n = 2 energy level according to the Bohr model. Use the Bohr model to determine the ionization energy of the He+ ion, which has a single electron. Also, calculate the minimum wavelength a photon must have to cause ionization.

Compton Effect Why is the sky blue? It is blue because molecules in the atmosphere collide with the incoming light causing it to scatter. A.H. Compton discovered that a photon that is scattered by electrons experiences some fundamental changes after the collision. American Physicist

The new wavelength of the photon is called the Compton wavelength.
The scattered photon has a longer wavelength which means: the frequency is lower the energy is lower Because the energy of the photon has decreased, the electron that it collided with gains energy (conservation of energy) The scattered photon also changes direction causing the electron to change direction (conservation of momentum) The new wavelength of the photon is called the Compton wavelength.

When a patient is exposed to photons of x-ray radiation in cancer treatments, most of the photons pass right through. Some photons undergo Compton scattering and leave energized electrons in the person’s body. These energized electrons can effectively destroy tumors in the person’s body

λ = h / p Wave Nature of Matter
Two examples of thinking “out of the box” Einstein proposed that light (which was understood as a wave) had particle-like properties Louis deBroglie theorized that all particles had wave-like properties In the same way that Einstein proposed that for photons: p = h / λ deBroglie proposed that for particles: λ = h / p French Physicist λ = deBroglie wavelength (m) h = Planck’s constant p = momentum of particle (kgm/s)

According to deBroglie, all particles (large and small, bowling balls and atoms) have waves around them. For example, the electrons around an atom move in a wavelike pattern around the nucleus. DeBroglie believed that the waves formed by the electrons could only move at the specific frequencies that formed standing waves.

If an electron was to move to an excited state, it would have to find the frequency that would form a new standing wave Any frequency that didn’t form a standing wave would cause the electron’s motion to die out. The frequencies of the excited states are multiples of the ground state.

Calculate the de Broglie wavelength of a 0
Calculate the de Broglie wavelength of a 0.20-kg ball moving with a speed of 15 m/s. Determine the wavelength of an electron that has been accelerated through a potential difference of 100 V.

Nuclear Physics The nuclei of atoms are composed of protons and neutrons. Protons have positive charge. Neutrons have no charge. This group of particles are called nucleons. You would expect protons to repel each other because of electrostatic forces (like charges repel). But they don’t. Inside the nucleus are forces that are much stronger than electrostatic forces. They are called strong nuclear forces.

Strong Nuclear Force Electrostatic Gravitational Weak Nuclear Force
Four Fundamental Forces in Nature Strong Nuclear Force Electrostatic Gravitational Weak Nuclear Force Found between nucleons at short distances Found between objects with electric charge Found between objects with mass Found between nucleons in radioactive decay Relative strength = 1 Relative strength = 10-2 Relative strength = 10-43 Relative strength = 10-13

The atoms of a specific element all have the same number of protons, but they have different numbers of neutrons. These various forms are called isotopes. Isotope notation allows us to know specifically what a nucleus contains. Z = atomic number (number of protons) A = mass number (number of nucleons) The difference between the two numbers is the number of neutrons.

Most isotopes in nature are stable, but some are unstable meaning they spontaneously decay and emit new particles. These unstable isotopes are called radioisotopes. Henri Becquerel discovered that when a radioactive sample was placed in a magnetic field, it emitted particles that were deflected in different directions? Some particles deflected left Some particles deflected right. Some particles didn’t deflect. What did he conclude? French Physicist

Alpha Decay Alpha decay occurs because there are too many protons in a nucleus causing excessive repulsion. Nucleus gets rid of a bundle of protons and neutrons called an alpha particle (positively charged). An alpha particle is a helium nucleus made up of two protons and two neutrons.

Example of the Alpha Decay of Radium - 226 into Radon - 222

Beta Decay Beta decay occurs when there are too many neutrons in a nucleus. Extra neutrons are changed into protons and electrons. Electrons that are emitted in these reactions are called beta particles (negatively charged).

Example of the Beta Decay of Cesium-137 to Barium-137

Gamma Decay Gamma decay occurs when an entire nucleus is in an energized state (after a previous radioactive decay). Energy is emitted in the form of photons that are called gamma particles. The atom experiences no change in mass.

Example of the various ways boron – 12 decays into carbon – 12
Example of the various ways boron – 12 decays into carbon – 12. It can either be beta decay or a combination of beta and gamma decay.

Nuclear Fission and Chain Reactions
Nuclear energy holds what many believe to be the key to solve the mounting energy crisis we face as a global community. Most of our energy comes from nonrenewable sources. The Earth’s climate may be in a warming period (debatable) which many believe to be a result of the burning of fossil fuels (also debatable) Because of #1 and possibly #2, there is good reason to investigate the more widespread use of nuclear energy (despite what happened in Japan)

Naturally-occuring uranium -235 is bombarded with neutrons.
The uranium – 235 absorbs the neutron to form uranium – 236 which is now in an excited state. The nucleus elongates because of the added neutron and the extra energy which causes the nucleons to move faster. The strong nuclear force weakens because of the new distance between nucleons. Electrostatic force increases causing nucleus to split into two new nuclei (X1 and X2) What results are two fission fragments along with a few individual neutrons. These new neutrons can, in turn, continue to bombard other uranium-235 atoms causing a chain reaction.

In a chain reaction, daughter particles and isolated neutrons are created. But mass is NOT conserved
Mass of products does not equal mass of reactants. Some of the mass is converted into energy

E = mc2 ΔE = Δmc2 Mass Defect
Albert Einstein’s most well-known in the area of particle physics was his introduction of the formula E = mc2 ΔE = Δmc2 E = energy (J) m = mass (kg) c = speed of light (m/s) Since c is constant, the formula shows that mass is simply a form of energy known as “rest energy”. In a sense, it is like potential energy. Because “c” is so large, the formula shows that a small change in mass is equivalent to a large change in energy. In a nuclear reaction, the masses of the products will be less than the masses of the reactants. This change in mass is known as the mass defect.

To calculate the mass defect, the actual masses of the subatomic particles have to be used.
Δm = mass of reactant particles – mass of product particles 1 u (atomic mass unit) = 1.66 x kg Either convert mass to kg and express energy in Joules or use: ΔE = 931.5Δm ΔE = energy (eV) Δm = (u)

What is the missing element X in the following fission reaction?
n + U  X + Sr n What is the mass defect of the above reaction? (find masses in Appendix B) How much energy is produced in each collision between a neutron and a uranium atom? 235 92 A Z 90 38 1 1