Question

Einstein's 1905 paper on the photoelectric effect was the first important application of Planck's quantum hypothesis. Describe Planck's original hypothesis, and explain how Einstein made use of it in his theory of the photoelectric effect.

Short answer

Planck's quantum hypothesis, introduced in 1900, states that the energy of an oscillating system is quantized, meaning it is available in discrete packets called "quanta". The energy of a single quantum is given by \(E = h \upsilon\), where \(h\) is Planck's constant and \(\upsilon\) is the frequency of the oscillation. Einstein applied this concept to the photoelectric effect, proposing that the energy of light is quantized in the form of particles called photons. This allowed him to predict key aspects of photoelectric behavior, such as the number of emitted electrons being proportional to the intensity of the incident light, the kinetic energy of the ejected electrons depending on the frequency of the light, and the existence of a threshold frequency for electron emission. These predictions were later experimentally confirmed, and Einstein's work on the photoelectric effect supported the quantization of energy and the development of quantum mechanics.

Step-by-step solution

Introduction to Planck's Quantum Hypothesis

Planck's quantum hypothesis was introduced in 1900 by Max Planck to solve the problem of blackbody radiation. According to classical physics, the energy distribution of a blackbody should be continuous. However, the experimental data showed that the energy distribution has a maximum at a certain frequency and then decreases again. Planck realized that the energy distribution could only be explained if energy was quantized.

Define Energy Quantization

Planck's quantum hypothesis states that the energy of an oscillating system, such as an electromagnetic wave, is quantized. That is, the energy is only available in discrete packets called "quanta". The energy of a single quantum is given by: \(E = h \upsilon\), where \(E\) is the energy of one quantum, \(h\) is Planck's constant and \(\upsilon\) is the frequency of the oscillation. This concept was revolutionary at the time because it challenged the classical concept of continuous energy distribution.

Introduction to the Photoelectric Effect

The photoelectric effect is the emission of electrons from a material (usually a metal) when it is exposed to light. Prior to Einstein's work, the classical understanding of the photoelectric effect was that the energy of the incident light waves would be absorbed by the electrons in the material and, if the energy was sufficient, the electrons would be ejected from the material.

Einstein's Application of Planck's Quantum Hypothesis to the Photoelectric Effect

Einstein proposed that the photoelectric effect could be explained by considering that the energy of light is not a continuous wave, but is quantized in the form of particles called photons. Each photon carries an energy equal to \(E = h \upsilon\), where \(\upsilon\) is the frequency of the light and \(h\) is Planck's constant.

The Key Predictions of Einstein's Photoelectric Effect Theory

Einstein's theory of the photoelectric effect made several key predictions based on Planck's quantum hypothesis: 1. The number of electrons emitted is proportional to the intensity of the incident light (meaning the number of photons striking the material). 2. The kinetic energy of the emitted electrons depends only on the frequency of the incident light, and not on its intensity. 3. There exists a threshold frequency below which no electrons are emitted, regardless of the light's intensity. This threshold frequency corresponds to the minimum energy required to release an electron from the material, called the work function.

Confirmation of Einstein's Theory of the Photoelectric Effect

The predictions made by Einstein's theory of the photoelectric effect were later experimentally confirmed, providing strong evidence in favor of Planck's quantum hypothesis. In 1921, Einstein was awarded the Nobel Prize in Physics for his work on the photoelectric effect that supported the quantization of energy, which formed the basis for the development of quantum mechanics.