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, developed in 1900, states that energy emitted by oscillating bodies is quantized and can only be in discrete integer multiples of a base value. This base value, called a quantum, is given by the relation \(E = nhv\), where \(n\) is an integer, \(h\) is Planck's constant, and \(v\) is the frequency of the radiation. Einstein applied this hypothesis to the photoelectric effect by proposing that light is composed of discrete energy packets called photons, with energy given by \(E = hv\). When a photon interacts with an electron on a metal surface, it transfers its energy to the electron. If this energy is greater than the electron's binding energy (or work function, \(W\)), the electron is ejected. The maximum kinetic energy of the emitted electron is given by \(K_{max} = hv - W\). This theory explained the observed properties of the photoelectric effect and earned Einstein the Nobel Prize in Physics in 1921.

Step-by-step solution

Describe Planck's original quantum hypothesis

Planck's quantum hypothesis was developed in 1900 by the German physicist Max Planck. He proposed a new model to describe the radiation emitted by a black body. According to his hypothesis, energy emitted by oscillating bodies can only be discrete, in terms of integer multiples of a certain base value, that is, the energy is quantized. The base value, called a quantum, depends on the frequency of the radiation (\(v\)) and a new constant, which later came to be known as Planck's constant (\(h\)), with the value of approximately \(6.626 \times 10^{-34}\:Js\). The energy (\(E\)) of any radiation is given by the relation: \[E = nhv\] where \(n\) is an integer.

Explain the photoelectric effect

The photoelectric effect is the phenomenon of releasing electrons from the surface of a material when light shines on it. When light with a certain threshold frequency or higher strikes a metal surface, electrons are ejected from the metal. This creates an electrical current, known as photocurrent. However, theories based on classical physics failed to explain some of the observed properties of the photoelectric effect, such as the dependence of the kinetic energy of emitted electrons on the frequency of incident light, and the independence of the number of emitted electrons on the intensity of the light. This discrepancy led to Einstein's utilization of Planck's quantum hypothesis to better explain the photoelectric effect.

Describe how Einstein made use of Planck's quantum hypothesis

In 1905, Albert Einstein applied Planck's quantum hypothesis to the photoelectric effect. He proposed that light itself is not a continuous wave, but rather a collection of discrete energy packets called photons. The energy of each photon is given by Planck's relation: \[E = hv\] Einstein theorized that when a photon interacts with an electron on the surface of a metal, the photon transfers its energy to the electron. If the energy transferred is greater than the electron's binding energy, also known as the work function (\(W\)), the electron is ejected. Consequently, the maximum kinetic energy (\(K_{max}\)) of the emitted electron is given by: \[K_{max} = hv - W\] Einstein's theory successfully explained the observed properties of the photoelectric effect, such as the dependence of the kinetic energy of emitted electrons on the frequency of incident light and the independence of emitted electrons on the intensity of the light. In 1921, Einstein was awarded the Nobel Prize in Physics for his work on the photoelectric effect and its connection to the quantum hypothesis.