### Video Transcript

The statements below describe experimental observations of processes involving electrons. Roman numeral (I) decelerating electrons emit light. Roman numeral (II) electrons are scattered from the surface of a metal, and a diffraction pattern is observed. Roman numeral (III) electrons are emitted from a metal surface that has been struck by photons, and the energy of the electrons is measured. (a) Roman numeral (II) only. (b) Roman numeral (III) only. (c) Roman numerals (I) and (II) only. (d) Roman numerals (I) and (III) only. (e) Roman numerals (I), (II), and (III). Which of the observations provides evidence that an electron needs a minimum energy to leave a surface?

Our problem asks us to analyze the above statements to determine which of these observations provides evidence that our electron needs a minimum energy to leave the surface. Let’s begin with Roman numeral number (I) decelerating electrons emit light.

In statement number (I), there is no discussion about the electron leaving a surface, nor is there any discussion about the energy of the electron. Therefore, this statement does not provide evidence that an electron needs a minimum energy to leave the surface. This allows us to eliminate any answer choices that include Roman numeral number (I). This would be answer choices (c), (d), and (e), which all include Roman numeral number (I) as an observation that provides evidence that the electron needs a minimum energy to leave the surface.

Roman numeral (II) states that electrons are scattered from the surface of a metal, and a diffraction pattern is observed. This statement does provide evidence of the electrons leaving a surface, but then goes on to discuss the wave nature of electrons by talking about the diffraction pattern. Whereas our problem wanted to know the minimum energy necessary to leave the surface. This tells us that this statement does not fully answer our question. And we can therefore eliminate any answer choices that have Roman numeral (II) in them.

Along with our previously eliminated answer choices (c), (d), and (e), we can also eliminate answer choice (a) Roman numeral (II) only as we have established that Roman numeral (II) does not fully answer our question. This leaves us with answer choice (b) Roman numeral (III) only. Let’s analyze Roman numeral (III) statement to ensure that it does provide the necessary evidence that an electron needs a minimum energy to leave a surface.

Roman numeral (III) states that electrons are emitted from a metal surface that has been struck by photons, and the energy of the electrons is measured. Just as in Roman numeral (II) and Roman numeral (III), there is evidence that our electrons leave a surface as the problem asked. The statement goes on to let us know that the energy of the electrons is measured as they are emitted. This statement describes the photoelectric effect. The photoelectric effect states that electrons are emitted from a material when the material absorbs light.

To understand this phenomenon better, we have drawn a graph of the energy of the electrons emitted versus the frequency of the light hitting the surface. Our 𝑥-intercept is the minimum frequency of incoming light that will emit electrons from our material. We call this the threshold frequency. Any light that hits this material with a frequency that is less than the threshold frequency will not emit any electrons. Looking at the part of the graph that contains frequencies of light that are all above the threshold frequency, we can see that as the frequency of incoming light increases, so does the energy of the emitted electrons.

We can therefore write an energy-conservation equation. The initial energy has to equal the final energy. The initial energy is the energy of the photons hitting the material as represented by 𝐸 subscript ph. Some of the energy gets absorbed by the material. This energy is known as the work function, as represented by the Greek letter Φ. The rest of the energy goes into the kinetic energy of the electrons, as represented by the letters KE. Let’s rearrange our formula to determine what the kinetic energy of these electrons is based off of.

To isolate KE, we must subtract the work function Φ from both sides of the equation. This will cancel out the work function on the right side of the equation. This leaves us with the expression the energy of the incoming photons minus the work function is equal to the kinetic energy of the emitted electrons. The work function, therefore, is the minimum amount of energy needed to emit electrons. Returning to Roman numeral number (III), when we measure the energy of the electrons, we can determine the work function of the material, as was shown in our energy conservation equation.

We can now say with confidence that answer choice (b) Roman numeral (III) only is the correct answer. As Roman numeral (III) is the only statement that provided evidence that an electron needs a minimum energy to leave the surface.