Question

Imagine two electrons on a plate of sodium metal. One electron is found right on the surface of the metal. The other electron is buried several layers below. A) The electron on the surface needs the least energy to escape due to its proximity to the surface. B) The buried electron needs the least energy to escape due to reduced surface interactions. C) Both electrons need the same amount of energy to escape. D) It's impossible for either electron to escape. Which electron will be moving faster when it absorbs the energy from a photon and escapes? Why? A) The surface electron will move faster due to less interference. B) The buried electron will move faster due to greater energy absorption. C) Both electrons will move at the same speed. D) The electron's speed depends on the energy of the photon absorbed.

Answer 1

The surface electron will move faster upon escaping because it requires less energy to overcome the surface potential and can thus retain more of the absorbed energy as kinetic energy. Energy levels and electron transitions are based on the principles laid out in Bohr's atomic model.

Step-by-step explanation:

The electron that will be moving faster when it absorbs the energy from a photon and escapes is the one that is on the surface of the sodium metal. The correct answer to this question is A) The surface electron will move faster due to less interference. This is because the surface electron needs less energy to escape from the metal due to its proximity to the surface (work function and photoelectric effect). Once the surface electron absorbs enough energy to overcome the binding energy, it will escape with the excess kinetic energy. The buried electron, on the other hand, would need additional energy to reach the surface before it can escape, so even if it absorbs the same amount of energy from a photon, it will spend part of this energy overcoming the additional attractive forces from the layers of atoms above it.

According to Bohr's model of the atom, when an electron jumps to a higher energy level, it absorbs energy, and when it falls back to a lower energy level, it releases energy in the form of electromagnetic radiation. This is relevant to the question because it explains how electrons can absorb energy (in this case from a photon) and what happens when they change energy states.

Moreover, the electron's speed after absorption does also depend on the energy of the photon absorbed; an electron on the surface that absorbs a photon with just enough energy to escape will have less kinetic energy than one that absorbs a photon with more energy than is necessary to escape the surface potential.

Answer 2

FOR BOTH PART OPTION A IS CORRECT.

The surface electron on the sodium metal plate will require the least energy to escape due to the work function being lower at the surface, and it will move faster upon absorption of a photon's energy since it will have more excess energy to convert into kinetic energy.

Step-by-step explanation:

When discussing which electron, the one on the surface of sodium metal or the one buried layers below, requires less energy to escape, it's essential to understand the concept of work function and photoelectric effect. The work function is the minimum amount of energy required to remove an electron from the surface of a metal. The electron on the surface is closer to overcoming the metallic bond and thus requires less energy to be ejected, making option A correct: The electron on the surface needs the least energy to escape due to its proximity to the surface.

Now, considering an electron that absorbs a photon's energy and escapes, its speed upon ejection will depend on the excess energy provided by the photon above the work function. Since the work function for the surface electron is less, any additional energy from the absorbed photon will contribute more to the kinetic energy of the surface electron. Therefore, option A is correct for the second part: The surface electron will move faster due to less interference.

In summary, the energy of the absorbed photon minus the work function is converted into the kinetic energy of the ejected photoelectron. It's also important to note that if the electrons do not absorb photons with enough energy to overcome the work function, neither will be ejected, regardless of their position within the metal.