A group of students investigated the reactions of several metals with solutions containing metallic ions.

Experiment 1

The students placed strips of a metal, X(s), into solutions containing different metallic ions, Ym+(aq), as shown in Figure 1.

Figure 1Metal strip in solution

After several hours, they observed whether or not Y(s) formed on the surface of the metal strip (see Table 1).

Table 1Results of Metal Strip Experiment

Experiment 2

The students placed a solid strip of each metal into an aqueous solution containing ions of the same metal. Complete circuits were established (Figure 2).

Figure 2Complete circuit

Finally, the students checked a general chemistry text to determine the standard reduction potentials for the following reactions.

Pb2+(aq) + 2e– → Pb(s)     E°red = –0.127 V

Reaction 1

Cu2+(aq) + 2e– → Cu(s)     E°red = +0.339 V

Reaction 2

The central nervous system is an example of an electrical system within the human body. Neurons are the basic electrical components of the central nervous system, and exist in three classes: sensory neurons, motor neurons, and interneurons. Each neuron is made of three main components: the nerve cell, the axons, and the dendrites. The longest axons are approximately 1 m in length, and the axon outer membrane is surrounded by an extracellular aqueous solution of protein, sodium, potassium, and chloride ions. A summary of the electrical properties of axons is shown in Table 1 and in Figure 1.

Table 1The Electrical Properties of Axons

Figure 1A segment of a simplified electric circuit model of the axon

Scientists can study the electrical properties of neurons by inserting probes into them to measure voltage changes as a response to stimulus. A typical plot of this action potential is shown in Figure 2.

Figure 2A typical nerve impulse, also known as the action potential

A nerve conduction velocity test (NCV) exploits the electrical properties of neurons to test for nerve damage. In this test, two electrodes are placed on a patient’s body, with an electrical shock placed on one and the nerve response measured on the other. The pulse travels at a constant speed of 100 m/s.

Researchers performed an experiment to investigate the thermal properties of human skin with regard to heat transfer. For this purpose an iron wire with known electric and thermal properties was mounted in a specially designed holder and placed 5 cm away from the forearm skin of a volunteer. The design enabled heat from the wire to be transferred to the skin. At room temperature the wire had a length L of 4 m, a diameter D of 4 × 10–4 m, and a mass M of 4 × 10–3 kg. The wire was connected in series with an ammeter, a power supply, and a switch.

The researchers selected a voltage (V) and closed the switch so current (I) flowed through the circuit, raising the wire’s temperature (T). The values in Table 1 were measured in five trials with different wire temperatures. (Note: The initial value of R, the circuit’s resistance, was measured at a temperature of 293 K with an ohmmeter. The other values of R were calculated from the values of V and L.)

Table 1Data for Thermal and Electrical Properties of Iron Wire

The change in wire length (ΔL) is related to the change in temperature (ΔT) by the relationship ΔL = αLΔT, where α, the coefficient of thermal expansion, is a constant. A similar relationship, ΔD = αDΔT, describes how the diameter of a wire changes when it is heated. The constant has the same value in both equations.

The energy radiated from a heated wire each second is AσT4, where A is the surface area of the wire, and σ = 5.67 × 10–8 J/m2·s·K4 is the Stefan·Boltzmann constant.

The most common cause of sudden cardiac arrest is ventricular fibrillation, an event in which the heart loses its electrical coordination. The only known cure for ventricular fibrillation is early defibrillation: a carefully timed electrical shock to the myocardium.

The principal component of a defibrillator is a capacitor. It is charged by placing the switch in Position C in Figure 1.

                                                  Figure 1  Schematic of a defibrillator

The capacitor consists of a pair of metal plates separated by a dielectric. During defibrillation the switch is placed in Position D, discharging the capacitor through paddles pressed against the chest of the patient. Firm force (~100 N) and a conductive gel pad are used to improve the electrical contact between each paddle and the patient’s chest.

For successful defibrillation the current delivered must be maintained for several milliseconds. Because the current in an RC circuit decays rapidly and exponentially, an inductor is added to the circuit to extend the duration of current flow.

Successful defibrillation also depends on the delivery of electrical charge to the myocardium. Only a fraction of the total current delivered by the defibrillator flows through the heart. The rest is dissipated by the resistance of the skin and the rest of the body. The resistances of the skin and the thoracic wall act as resistances in series, and the resistance of the other intrathoracic structures acts as a resistance in parallel with that of the myocardium.

A vacuum photodiode detector utilizes the photoelectric effect to detect light. The photoelectric effect causes electrons to be ejected from a metal plate when photons of light are absorbed by the metal. The energy of a photon is given by the equation E = hf, where h = 6.6 x 10-34J·s (Planck’s constant), and f is the frequency of the photon. To free an electron, the energy of a photon must be greater than a quantity called the work function of the metal. The ejected electron will have a kinetic energy equal to the photon’s energy minus the work function.

A vacuum photodiode is constructed by sealing two electrodes, a cathode and an anode, in a vacuum tube. The electrodes are separated by a distance, L = 0.01 m, and connected to a battery and a resistor, R = 100 Ω, as shown in Figure 1. The cathode is made of a photoelectric metal and is connected to the negative terminal of the battery. The potential difference between the cathode and anode is approximately equal to the battery voltage, V = 50 V. The electric field at all points between the electrodes is equal to the electrode voltage difference divided by L. The potential energy of an electron immediately after it is released from the cathode is equal to qV, where q = -1.6 x 10-19C is the charge of an electron. The work function for the vacuum photodiode is 2 x 10-19J.

Students constructed the electrical circuit shown below to study capacitors. A battery with a voltage of 10 V is connected through a switch to a capacitor and a 500-Ω resistor. The capacitor is constructed from two flat metal plates, each with a surface area of 5.0 × 10–5 m2. The plates are separated by 1.0 × 10–3 m, and the space between the plates is a vacuum. The connecting wires have no resistance. After the switch is closed and the capacitor is fully charged, a particle with a charge of 8.0 × 10–19 C and a speed of 1.0 m/s is injected midway between the capacitor plates.

A capacitor is a device that stores charge. The voltage V across a capacitor and the charge q on the capacitor are related by q = CV, where C is the capacitance measured in farads, F (1.0 F = 1.0 coulomb per volt).
 A student sets out to measure the capacitance using the circuit of Figure 1.

Figure 1Circuit for measuring capacitance

In this circuit, the capacitor will be fully charged soon after switch S is closed to the left, as current passes through the small fixed resistor r in series with the capacitor C. Then, when S is switched to the right, the capacitor discharges through the variable resistor R. R is adjusted so that the discharge current, as measured by the ammeter, is constant during the discharge time.

Figure 2The discharge current versus time

Figure 2 shows the current-versus-time plot during the discharge. The voltage of the battery used in the measurement was 12.0 V. The total charge q transferred to the capacitor can be estimated from the constant current value during the discharge time.