A metal surface of threshold frequency \(5.3 \times 10^{14} \mathrm{sec}^{-1}\) is exposed to a photon of radiation having energy \(3.5 \times 10^{-19} \mathrm{~J}\). Will it exhibit photoelectric effect?

When we delve into the world of quantum physics, Planck's equation is a crucial formula that serves as a bridge between the phenomena of light as particles and waves. In its essence, the equation connects the energy of a photon to its frequency. The equation is elegantly simple:

\( E = h u \), where \( E \) represents the energy of a photon, \( h \) is Planck's constant (6.626 \times 10^{-34} \mathrm{J \cdot s}), and \( u \) is the frequency of the photon.

• Planck's constant is a fundamental quantity in quantum mechanics, and it essentially dictates the scale of quantum effects.
• Frequency, denoted as \( u \), is the number of waves that pass a certain point per unit of time, measured in hertz (\mathrm{s}^{-1}).

As we talk about the photoelectric effect, Planck's equation is used to calculate the energy of photons to determine if they have sufficient energy to release electrons from a metal surface. The seemingly humble equation is foundational to understanding not just the photoelectric effect, but the entire quantum realm.

Every metal with a surface capable of exhibiting the photoelectric effect has a threshold frequency. It is the minimum frequency of incident light required to emit an electron from the metal's surface. Imagine it as the 'entry fee' of energy that a photon must pay to kick out an electron from its metal 'home'.

The threshold frequency, denoted as \( u_0 \), is a physical property intrinsic to the material of the metal and is determined experimentally.

• If the frequency of the incident light is below the threshold frequency, the electrons will not be ejected, irrespective of the intensity or duration of the light.
• If the frequency meets or exceeds the \( u_0 \), electrons can be liberated if photons carry enough energy.

To find out if the photoelectric effect will occur, a comparison between the photon's energy (calculated using Planck's equation) and the energy corresponding to the threshold frequency is imperative. This relationship is the cornerstone for understanding why certain materials react differently to light in the photoelectric experiment.

Exploring the photon energy further, it is the amount of energy carried by a single photon. The energy of a photon is quantized, meaning it can be thought of as a 'packet' of energy with a discrete value. How much energy each photon carries is pivotal in experiments such as the photoelectric effect.

• In the context of the photoelectric effect, the energy of the photons must be equal to or greater than that of the threshold energy in order to eject an electron.
• The concept of photon energy is also essential across various technologies like solar panels, where photons are absorbed to create electrical energy.

The energy of a photon is given by Planck's equation, and when we examine it alongside the threshold frequency, we come full circle in understanding the criteria for the occurrence of the photoelectric effect. Solving textbook problems often includes computing photon energy to predict whether or not an incident light will induce this phenomenon, harnessing the basic principles we've examined here.