Suppose that in the photoelectric-effect experiment we make a plot of the detected current versus the applied potential difference. What information do we obtain from such a plot? Can we determine from it the value of Planck's constant? Can we determine the work function of the metal?

When studying the photoelectric effect, the relationship between detected current and applied voltage reveals critical information about electron behavior. A graph plotting the current against the voltage illustrates how these two variables interact. As voltage increases, the electric field propels more electrons towards the detector, augmenting the current until it reaches a saturation point. Contrarily, negative voltage implies a repulsive force, causing the current to decline until reaching a point where no electrons are collected, known as the 'stopping voltage'.

Understanding this dynamic supports the comprehension of electron emission and energy levels needed to overcome the attractive forces within the metal, ultimately influencing the current detected in an experiment.

The determination of Planck's constant, denoted as 'h', is a pivotal aspect of quantum mechanics and the photoelectric effect provides a method for its empirical estimation. To calculate Planck's constant, one must have access to stopping voltage values for varying frequencies of incident light. By plotting these voltages against their corresponding frequencies, a linear relationship emerges, with the slope representing the ratio of Planck's constant to the charge of an electron, or \( \frac{h}{e} \). From this linear fit, one can deduce the value of 'h'.

This process showcases the direct relationship between energy (quantified through frequency) and the stopping voltage, a reflection of the energy threshold for the photoelectric emission, framing the foundational concept of quantized energy in physics.

The work function is an intrinsic property of a metal that is key to understanding the photoelectric effect. It represents the minimum energy necessary to liberate an electron from the metal's surface. This threshold varies among different materials based on their atomic structure. In the photoelectric experiment, one can calculate the work function, denoted by \( \Phi \), using the stopping voltage (\(V_s\)) obtained from the current vs. voltage plot. The equation \( \Phi = eV_s \), where 'e' is the electron charge, bridges the gap between an abstract concept (work function) and measurable quantities (voltage).

Knowing a material's work function is essential for applications in electronics and photovoltaics, as it directly affects the efficiency of electron emission under light exposure.

Stopping voltage is a fundamental parameter in the analysis of the photoelectric effect. It is the specific applied voltage at which no current is detected because all photoemitted electrons are repelled back to the metal surface. In essence, it's the point of equilibrium where the kinetic energy of the emitted electrons is precisely countered by the electric potential energy from the applied voltage.

From a practical perspective, determining the stopping voltage enables us to calculate both the work function and Planck's constant. Its importance cannot be overstated, as it is directly linked to the energy properties of emitted electrons and therefore dictates the transfer of energy from photons to electrons.