Photons and the photoelectric effect

• Quanta: Light being emitted as individual packets of energy called quanta.

• Photon: A quantum of electromagnetic energy is known as a photon

• Photoelectric effect: light behaves like a stream of photons, and this is

  illustrated by the photoelectric effect

• Photoelectrons: the released electrons are known as photoelectrons

• Wave theory of light predicted three results:

  • Significant time delay between the moment of illumination and the ejection of photoelectrons.

  • Increasing the intensity of the light could cause the electrons to leave the metal surface with greater kinetic energy.

  • Photoelectrons would be emitted regardless of the frequency of the incident energy, as long as the intensity was high enough.

• These predictions were not observed.

  • As, photoelectrons were ejected within a few billionths of a second after illumination, disproving the prediction.

  • Increasing the intensity of the light did not cause photoelectrons to leave the metal surface with greater kinetic energy.

  • For each metal there was a certain threshold frequency

• E = hf

  • h is the Planck’s constant = 6.63 x 10^-34 J/s.

• Metal’s work function is the certain amount of energy that has to be imparted to an electron on the metal surface

• K_max = hf -ϕ

• f_o = ϕ/ h

• SI unit for energy is the joule

Example

• The work function, ϕ_, aluminum is 4.08 eV

  • (a) What is the threshold frequency required to produce photoelectrons from

    aluminum?

    (b) Classify the electromagnetic radiation that can produce photoelectrons.

    (c) If light of frequency f = 4.00 × 1015 Hz is used to illuminate a piece of

    aluminum,

    (i) what is Kmax, the maximum kinetic energy of ejected photoelectrons?

    (ii) what’s the maximum speed of the photoelectrons? (Electron mass = 9.11×

    10−31 kg.)

    (d) If the light described in part (b) were increased by a factor of 2 in intensity,

    what would happen to the value of Kmax?

Solution

The Bohr Model of the atom

• The light from a glowing gas, passed through a prism to disperse the beam

  into its component wavelengths, produces patterns of sharp lines called

  atomic spectra.

• 

• R is Rydberg constant = 1.1 x 10^-7

• The electron absorbs a certain amount of energy, and it is excited to a higher

  orbit, emitting a photon in the process.

• The wavelength of the photon

• 

Example

• The first five energy levels of an atom are shown in the diagram

  below:

  (a) If the atom begins in the n = 3 level, what photon energies could be

  emitted as it returns to its ground state?

  (b) What could happen if this atom, while in an undetermined energy state,

  were bombarded with a photon of energy 10eV?

Solution

Wave-Particle Duality

• The electromagnetic radiation propagates like a wave but exchanges energy

  like a particle. This is known as wave-particle duality.

• De-Broglie Wavelength

• 

Example

• Electrons in a diffraction experiment are accelerated through a

  potential difference of 200 V. What is the de Broglie wavelength of these

  electrons?

Solution

The Wave Function

• The probability that a particle will be measured to be at a particular position

  when the position is measured. That probability is related to a new physical

  parameter called the wave function.

Relativity

• The Theory of relativity has only two postulates:

  • The results of physical experiments will be the same in any

    non-accelerating reference frames.

  • The speed of light is constant

• Time dilation:

  • Demonstrated by synchronized atomic clocks.

  • E.g: When a clock placed on a fast-moving airplane is compared to a clock at rest on the ground, the clock in the airplane shows that less time has passed than the time recorded by the clock on the ground.

    This is known as time dilation.

• Length Contraction:

  • To be consistent with time dilation, there must also be disagreement

Nuclear Physics

• The nucleus of an atom is composed of particles, protons, and neutrons.

• Protons + Neutrons = Nucleons

• The number of protons in a given nucleus is called the atom’s atomic number

  denoted by Z.

• The total number of nucleons (Z+N), is called the mass number, and is

  denoted by A.

• Isotopes: The nuclei that contain the same numbers of neutrons are called

  isotopes

• Notation

Example

• How many protons and neutrons are contained in the nuclide ?

Solution

• The subscript (the atomic number, Z) gives the number of protons, which is

  29. The superscript (the mass number, A) gives the total number of nucleons.

  Since A = 63 = Z + N, we find that N = 63 − 29 = 34

The Nuclear Force

• The strong nuclear force is a fundamental force that binds neutrons and

  protons together to form nuclei.

Binding Energy

• The masses of the proton and neutron:

  • Proton: 1.6726 x 10^-27 kg

  • Neutron: 1.6749 x 10^-27 kg

• Mass defect: The difference between the mass of any bound nucleus and the

  sum of the masses of its constituent nucleons is called the mass defect.

• E = mc^2

• Binding energy tells us how strongly the nucleus is bound

• 

Example

• What is the maximum wavelength of EM radiation that could beused to photodisintegrate a deuteron?

Solution

• The binding energy of the deuteron is 2.23 MeV,

  so a photon would need to have at least this much energy

  to break the deuteron into a proton and neutron. Since E =

  hf and f = c/λ

Nuclear Reactions

• Nuclear fusion: It is of small nuclei at extremely high temperatures.

• Nuclear fission: The emission of a particle or splitting of the nucleus

Alpha Decay

• When a nucleus undergoes alpha decay, it emits an alpha particle, which

  consists of two protons and two neutrons.

• It is the same as the nucleus of a helium-4 atom.

• An alpha particle can be represented as

• Two important features of a nuclear reaction:

  • Mass number is conserved.

  • Charge is conserved.

• The decaying nuclide is known as the parent.

• The resulting nuclide is known as the daughter.

Beta Decay

• There are three categories of beta decay, called β+, β−, and electron capture.

• β− decay:

  • When the neutron-to-proton ratio is too large, the nucleus undergoes

    β− decay.

  • It occurs when a neutron transforms into a proton and releases an

    electron. The expelled electron is called a beta particle.

  • The transformation of a neutron into an electron and a proton, and

    another particle called the electron antineutrino is caused by the

    action of weak nuclear force.

• β+ decay:

  • When the neutron-to-proton ratio is too small, the nucleus will undergo

    β+ decay.

  • In this form of β+ decay, a proton is transformed into a neutron and a

    positron, and another particle is called electron-neutrino.

• Electron Capture:

  • In which a nucleus can increase its neutron-to-proton ratio to capture

    an orbiting electron and then cause the transformation of a proton into

    a neutron

Gamma Decay

• In each of the decay processes defined above, the daughter was a different

  element than the parent. By contrast, gamma decay does not alter the identity

  of the nucleus; it just allows the nucleus to relax and shed energy.

• It must emit energy in the form of a photon or a gamma ray.

Example

• A mercury-198 nucleus is bombarded by a neutron, which causes a

  nuclear reaction: What’s the unknown product particle, X?

Solution

• In order to balance the superscripts, we must have 1 + 198 = 197 + A, so A = 2, and the subscripts are balanced if 0 + 80 = 79 + Z, so Z = 1:

• 

Conclusion

Disintegration Energy

• Nuclear reactions must conserve total energy.

• It involves the emission or absorption of energy.

• A general nuclear reaction is written as:

  • A + B —> C + D + Q

  • Q is disintegration energy

    • If Q is positive then the reaction is exothermic.

    • If Q is negative then the reaction is endothermic