QCM : Electrochemical Redox Reactions — 11 questions

Explication

Electrode (B) functions as the anode where water molecules are oxidized to produce oxygen gas, as stated in the source excerpt. Electrode (A) reduces Pb²⁺ ions, while the other options do not match the described electrode (B) role. Review: Electrolysis of lead nitrate solution and electrode reactions. Course evidence: "At electrode (A), which acts as the cathode, Pb²⁺ ions in solution are reduced by gaining electrons to form metallic lead deposits. At electrode (B), which acts as the anode, water molecules are oxidized, producing oxygen gas."

Explication

The conjugate base formed after titration remains dissolved and affects the pH beyond the equivalence point, as it results from deprotonation of propanoic acid and is the predominant species in solution at that stage. Review: Acid-base reactions of propanoic acid with sodium hydroxide and ethanol. Course evidence: "After the titration reaches the equivalence point, the predominant species in solution is the conjugate base, A⁻, which results from the deprotonation of propanoic acid. This conjugate base remains in solution and influences the pH beyond the equivalence…"

Explication

The source states that the fusion reaction combines deuterium and tritium to form helium and a neutron, and the mass defect between reactants and products is converted into energy according to E=Δmc², making this the primary role of the fusion reaction. Review: Nuclear fusion reaction of deuterium and tritium producing helium and associated energy calculations. Course evidence: "The fusion reaction combines deuterium (2H) and tritium (3H) to form helium (4He) and a neutron. The mass defect between the reactants (deuterium and tritium) and the products (helium and neutron) is converted into energy, as described by the relation E=Δmc²."

Explication

The decay law describes that activity decreases exponentially over time based on half-life; thus, using the initial activity and half-life allows precise calculation of activity at any time. Multiplying by time or simple division/addition do not follow the decay law and yield incorrect results. Review: Radioactive decay and activity calculations of tritium samples. Course evidence: "The activity of a radioactive sample decreases exponentially over time according to its half-life. This means that after each half-life period, the activity is reduced to half of its previous value. Using the initial activity and the activity after a known…"

Explication

The time constant \u03c4 in an RC circuit is defined as \u03c4 = R*C and it indicates the time needed for the voltage across the capacitor to reach approximately 63.2% of its final value during charging, as explicitly stated in the source excerpt. Review: Charging behavior and differential equations of an RC dipole circuit. Course evidence: "This constant indicates the time needed for the voltage to reach approximately 63.2% of its final value during charging."

Explication

Sustained oscillations are maintained by adding a voltage source proportional to the current, which replenishes the energy lost due to resistive damping, as described in the source excerpt. Increasing resistance or removing the inductor would not sustain oscillations, and decreasing capacitance affects period but not energy maintenance. Review: Damping and sustained oscillations in series RLC circuits with energy considerations. Course evidence: "Energy Dissipation and Maintenance : energy in the circuit decreases over time because of resistive losses, quantified by the energy difference (ΔE) between two points in time; energy can be replenished by adding a voltage source proportional to the current,…"

Explication

The Lorentz force is defined as a vector force exerted on a charged particle moving in a magnetic field, expressed as F = q (v × B), and it is perpendicular to both the particle's velocity and the magnetic field. This distinguishes it from gravitational or electric forces and from scalar quantities like energy. Review: Lorentz force and motion of charged particles in a uniform magnetic field. Course evidence: "Force de Lorentz : A vector force exerted on a charged particle moving in a magnetic field, given by F = q (v × B), perpendicular to both velocity and magnetic field."

Explication

The trajectory radius is directly related to the particle’s mass-to-charge ratio, and by comparing measured radius ratios with known ion masses, it enables identification of unknown ions. The other options describe different measurements not linked to the role of trajectory radius described in the source. Review: Determination of particle trajectories and identification in magnetic fields. Course evidence: "The radius of the trajectory is directly related to the particle’s mass-to-charge ratio, with particles of the same charge but different masses exhibiting different radii under identical magnetic conditions. Comparing the measured radius ratios of particles…"

Explication

The small angle approximations sin θ ≈ θ and cos θ ≈ 1 - θ²/2 are used to simplify the energy expressions of the pendulum, making the analysis of its motion easier, as stated in the source. Review: Energy analysis of a simple pendulum under small oscillations. Course evidence: "For small angles, sin θ ≈ θ and cos θ ≈ 1 - θ²/2, simplifying energy expressions."

Explication

Energy diagrams relate kinetic and potential energy at different pendulum positions, allowing calculation of maximum angular displacement by identifying where kinetic energy is zero and potential energy is at its maximum. Review: Calculation of mechanical energy and angular displacement in pendulum motion. Course evidence: "Maximum angular displacement, θmax, can be determined from energy diagrams that relate kinetic energy to potential energy at different positions of the pendulum. These diagrams illustrate how energy shifts between kinetic and potential forms during…"

Explication

The angular displacements θ1 and θ2 correspond to the points where potential energy equals kinetic energy, marking key phases of energy equilibrium during pendulum oscillations as energy transfers between forms. Review: Relationship between potential and kinetic energy in pendulum oscillations. Course evidence: "During pendulum oscillations, at certain angular displacements θ1 and θ2, the potential energy stored in the pendulum equals its kinetic energy. This indicates that energy is continuously exchanged between these two forms as the pendulum swings back and…"