Students are given an assignment to create a circuit from a given set of components. Four different students create circuits in unique manners and the professor measures the resistance of the circuit, the power output of the circuit and the heat given off by each circuit after each circuit was running for a certain amount of time. Circuits with resistors in parallel have a lower total resistance than those that have resistors in series.

What other important information should be noted by the professor? 

Scientist 1: Scientist 1 believes that light displays particle behavior. This means that rays of light have their own associated momentum. Furthermore, Scientist 1 does not believe that light will exhibit wave behavior.

Scientist 2: Scientist 2 disagrees with Scientist 1 and believes that light can exhibit wave behavior, but does not display particle behavior. In other words, this scientist believes that light does not have any momentum.

Experiment: To settle their disagreement, the scientists setup the following experiment. The scientist take dark metallic material. This material is attached to pole and the metallic material can spin if it is subjected to a force; similar to a watermill or wind turbine. This setup is then placed outside and exposed to sunlight. 

What is a potential issue with this experiment?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

The value corresponding to the binding energy of an electron to its positively charged nucleus is known as the work function, and corresponds to the y-intercept of the trend line produced when frequency of incident light is graphed against kinetic energy of liberated electrons. What is the work function for copper?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

Figure 2 shows that the threshold frequency, in Hertz, for copper is most nearly:

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

An electron has a negative electric charge of . How many electrons are produced per photon with the frequency stated in Experiment 2?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

The circuit setup in Experiment 3 can be considered a solar cell as electricity is produced when the wire collects electromagnetic radiation. An important consideration in the development of solar cells is their efficiency, which can be defined as the ratio of electrons produced to photons incident on the material expressed as a percentage. What is the efficiency of the solar cell in Experiment 2? 

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

Why did the scientist hold the frequency of x-rays at  in Experiment 2?

A scientist observed that when low energy types of electromagnetic radiation (light), such as visible light or ultraviolet light, were shone onto a conductive copper wire incorporated into a circuit with a light bulb as shown in Figure 1, the light bulb did not come on. However, when electromagnetic radiation of a higher energy, such as x-rays or gamma rays, was shone onto the wire, the light bulb did come on, indicating a current (electricity) was produced in the wire. The scientist hypothesized that this effect was due to the fact that electromagnetic radiation of a certain energy was able to overcome the attraction between electrons and protons in the individual atoms of copper in the wire, and liberate an electron to produce the electric current. He called this the photoelectric effect, and did the following experiments to further study this effect.

Figure 1

Experiment 1:

The scientist put a sample of copper in an instrument that can measure the energies of free-moving electrons. He shone a light source capable of producing specific energies of electromagnetic radiation on the metal and slowly increased the energy of the light. The instrument was used to measure the kinetic energies (energy due to motion) of any electrons that were liberated from the copper sample. The scientist recorded the energy of light used in frequency, where a low frequency corresponds to a low energy electromagnetic radiation, and a high frequency corresponds to a high frequency of electromagnetic radiation. He saw that no electrons could be detected at low frequencies, and that after a specific frequency he called the threshold frequency, the kinetic energy of liberated electrons increased linearly with increasing frequency of incident light as shown in Figure 2 below. The data was fitted with a line along which the data falls; the equation describing this line is shown in Figure 2.

Figure 2

Experiment 2:

The scientist removed the light bulb from the circuit shown in Figure 1 and replaced it with an instrument that can measure electrical charge. He then directed his x-ray source at the wire and slowly increased the intensity of the X-ray light while the frequency was held constant at . He monitored the current produced in the wire as the intensity of light increased and recorded the results in Figure 3 below. Intensity of light is measured in photons (a discrete particle, the fundamental unit of light) and charge in Coulombs, and like in Experiment 1, a linear equation is fitted to the data and shown in Figure 3.

Figure 3

What is the meaning of the slope in the regression equation for the data shown in Figure 1?

Experiment 1

A scientist develops the following setup, shown in Figure 1 below, to study the charges of radioactive particles. A radioactive sample is placed into a lead box that has an open column such that the particles can only exit from one direction. A detector is placed in front of the opening. A metric ruler (centimeters (cm)), is aligned on the detector such that zero is directly in front of the opening of the column, with the positive values extending to the left and the negative values to the right. On the left side of the experimental setup, there is a device that generates a magnetic field that attracts positively charged particles and repels negatively charged particles.

                                                    Figure 1.

The device detects particles in three different places: alpha, α; beta, β; and gamma, γ; as labeled in Figure 1. The paths these particles take from the source of radioactivity are shown.

Experiment 2

A different scientist finds the following data, shown in Table 1, about the energies of the α, β, and γ particles by observing what kinds of materials through which the particles can pass. This scientist assumes that the ability of particles to pass through thicker and denser barriers is indicative of higher energy. Table 1 summarizes whether or not each type of particle was detected when each of the following barriers is placed between the radioactivity source and the detector. The paper and aluminum foil are both 1 millimeters thick, and the concrete wall is 1 meter thick.

Why did the scientist in Experiment 2 include a test with no barrier?

Laura is performing an experiment with a 5kg weight tied to a 3m rope tied to the ceiling as shown:

Laura drops the weight and allows it to swing freely. She measures how long it takes for the weight to return to it's original position (assume no forces outside of gravity are acting upon the pendulum). This is also called one oscillation.

Experiment 1:

Laura created the following table for her first measurement of the pendulum's oscillations.

Experiment 2:

Laura performed the experiment again, this time using a 6kg weight.

 Experiment 3:

Laura performed the experiment again, this time using a 3kg weight and a 5m rope.

How long would 4 oscillations be, using the 3m rope and the 6kg weight?