SAT Physics Atomic and Quantum Phenomena - Ionization Energy/Work Function

SAT Physics Atomic and Quantum Phenomena - Ionization Energy/Work Function

In energy level problems, electrons receive just enough energy to reach a higher energy level inside the atom. However, if the energy of the incoming photons is greater than the energy difference between the ground state and the edge of the atom, then the electrons are ejected from the atom. In this process, the atom becomes a positive ion. The minimum energy required to accomplish this is known as the ionization energy. For atoms with electrons in the ground state, the ionization energy is equal to the absolute value of the ground state energy. For hydrogen gas with a ground state of -13.6 electron volts, the ionization energy is equal to 13.6 electron volts. The ionization energy is the minimum energy needed to eject an electron and ionize an atom. The ionization energy is also known as the work function, Φ.

The photoelectric effect involves the ionization of atoms by striking them with photons that exceed the energy difference between the ground state and the edge of the atom. Figure 20.6 shows a hypothetical atom with a ground state of -10 electron volts that is radiated by photons with 12 electron volts of energy.
Figure 20.6. The photoelectric effect

If these energies are added in the same manner as in the previous section, the result is a positive energy instead of a negative energy.
Eelectron initial + Ephoton = Eelectron final = (-10 eV) + (-12 eV) = 2 eV

   Electrons with positive energies have been ejected from the atom. This electron will leave the atom. When it does, the electron will have 2 electron volts of energy. The ejected electron will be moving with this excess energy, which is known as the maximum kinetic energy,Emax, of the ejected electron. In order to be ejected, the electron first had to move from the ground state, -10 electron volts, to the edge of the atom, 0 electron volts. This required the addition of 10 electron volts of energy. The energy to move from the ground state to the edge of the atom is known as the work function, Φ. The work function is essentially the absolute value of the ground state energy. For the atom in Figure 20.6, the work function is:
  The excess energy of the ejected electrons can be determined as follows:
Kmax = Ephoton - Φ
  The energy of a photon is related to its frequency, Ephoton = hf. This expression can be substituted into the previous equation to complete the equation for the photoelectric effect:
Kmax = hf - Φ
  Both versions of this formula may be encountered. In Figure 20.6, the energy of the incident photon was given. So the first formula, Kphoton - Φ, is used.
Kmax = (12 eV) - (10 eV) = 2 eV

  What is the significance of moving, ejected electrons? When certain metallic substances with low work functions are radiated with high-energy photons, countless electrons are ejected. These electrons are in motion. A lot of moving electrons comprise a current. As a result, this phenomenon is a way to generate an electric current using photons of light. It is known as the photoelectric effect since it converts photon energy to electric energy. This is how electricity is generated using sunlight. The photoelectric effect is at the heart of solar power.
   A photocell is a battery-like photoelectric apparatus. Like a battery, a photocell consists of two metal plates. One of the plates is composed of a metal with a low work function that will easily emit electrons, e, when radiated with photons. Figure 20.7 depicts a photocell being radiated with photons.
Figure 20.7. Photocell

   Each atom in the plate radiated by the photons ejects electrons, which move with kinetic energy, Kmax, toward the opposite plate. The plate radiated with photons loses electrons and becomes positive. The plate receiving the excess electrons becomes negative. This creates a potential difference, V, between the plates. Energy is conserved during this process. The kinetic energy of the electrons Kmax, is converted into electric potential energy, UE.
UE = Kmax
   When a wire is connected between the plates, the potential difference provides the pressure to move electrons from the negative plate to the positive plate. Note that usually current is regarded as the flow of positive charges. However, the photoelectric effect focuses on the released electrons and tracks the actual electron flow, which is technically a negative current.
The photoelectric effect experiment consists of a photocell, an ammeter, and a variable power supply connected in series as shown in Figure 20.8.
Figure 20.8. Photoelectric effect experiment

   The variable power supply (battery symbol with an arrow running through it) creates a second potential difference in addition to the potential difference produced in the photocell. The power supply is wired into the circuit backward, so its electric potential can cancel the electric potential generated by the photocell. This experiment is not about creating solar power. Instead, it is designed to measure and test the properties of the photoelectric effect. The ammeter records the amount of current flowing in the circuit. In the experiment light with different frequencies (energy) and intensities (brightness) are use to stimulate the photocell. When the variable power supply is adjusted so that the ammeter reads zero, no current is flowing in the circuit. This occurs when the potential (electric pressure) of the photocell, pushing electrons counterclockwise in the circuit, is equal to the potential of the power supply, which is pushing electrons clockwise in the circuit. The voltage displayed by the adjustable power supply is known as the stopping potential, since it stops current from flowing. The stopping potential of the power supply equals the potential induced in the photocell when the current is no longer flowing. When the ammeter reads zero:
Vphotocell = Vs
Several key observations were made as the frequency of the photons incident on the photocell was steadily increased.
  1. Photons with very low frequencies created no potential in the photocell, indicating that no electrons were ejected.
  2. As the frequency of the photons was steadily increased, a threshold frequency was encountered that induced a potential in the photocell, indicating that electrons were starting to flow.
  3. Increasing the frequency of the photons above the threshold frequency increased the potential of the photocell and the energy of the emitted electrons. The increase in the energy of the emitted electrons was linear and matched the following equation:
Kmax = hf - Φ
   The results of the photoelectric effect experiment are summarized in a graph of electron energy versus photon frequency shown in Figure 20.9.
Figure 20.9. Kmax versus frequency

   The graph of the photoelectric effect is a linear graph of the kinetic energy equation. If it is compared with the equation for a line, several key facts stand out.
Photoelectric effect : Kmax = hf- Φ
Equation of a line : y = mx + b
  • The slope of the graph is Planck’s constant, h.
  • The work function, Φ, has the same value as the y-intercept but has the opposite sign. The y-intercept of the photoelectric effect is negative, so the work function is the absolute value of the y-intercept.
  • The threshold frequency occurs at a point where is equal to zero. This fact can be used to determine the work function, Φ, when given the threshold frequency, f0.
Kmax = hf- Φ
      (0) = hf0 - Φ
  Φ = hf0
   In another experiment, the photon frequency was held at a constant value. That value was capable of ejecting photons. Instead, the intensity of light was varied. This experiment yielded different results.
  1. Increasing the intensity of light increases the number of photons incident on the photocell. When more photons strike the photocell, more electrons are ejected.
  2. Increasing the light intensity does not change the voltage of the photocell or the energy of the ejected electrons.
  3. If the power supply is adjusted to zero, the voltage of the photocell will cause a current to flow. Increasing the intensity of light increases the current flowing in the circuit.
The observations recorded in the photoelectric effect experiment indicate that light acts as a particle rather than as a wave.


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