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 original quantum hypothesis, formulated in 1900, proposed that energy is quantized and comes in discrete amounts. The energy of a photon is given by \(E = h\nu\), where \(h\) is Planck's constant and \(\nu\) is the frequency of radiation. Einstein applied this hypothesis in his 1905 paper on the photoelectric effect, which explains the emission of electrons from a surface when exposed to electromagnetic radiation. He proposed that light consists of photons with quantized energy, and the maximum kinetic energy of emitted electrons is described by the equation \(KE_{max}=hf-\phi\), where \(f\) is the frequency of the incoming photons and \(\phi\) is the work function. Einstein's theory of the photoelectric effect was the first significant application of Planck's quantum hypothesis, connecting it to the interaction of light with matter.

Step-by-step solution

1. Planck's Quantum Hypothesis

Planck's original quantum hypothesis was formulated by Max Planck in 1900. The hypothesis came as a result of his attempts to solve the problem of black-body radiation. Planck proposed that energy is quantized, which means it comes in discrete amounts rather than as a continuous flow. According to Planck's hypothesis, the energy of radiation is proportional to its frequency. The energy (E) of a single quantum, also known as a photon, can be defined as follows: \[E = h\nu\] where \(E\) is the energy of the photon, \(\nu\) is the frequency of radiation, and \(h\) is Planck's constant (approx. \(6.626 \times 10^{-34}Js\)).

2. Einstein's Theory of the Photoelectric Effect

In 1905, Albert Einstein published a paper on the photoelectric effect, which is the emission of electrons from a surface when it is exposed to electromagnetic radiation like light. According to classical physics, the energy of the emitted electrons should depend on the intensity of the light, rather than its frequency. However, experimental results contradicted this prediction. Einstein proposed that light consists of discrete packets of energy called photons, and the energy of these photons is quantized, as suggested by Planck's hypothesis. He further explained that when a photon with sufficient energy collides with an electron in a material, it can transfer its energy to the electron, enabling the electron to escape from the material surface. This phenomenon is known as the photoelectric effect. Einstein's equation for the photoelectric effect is: \[KE_{max}=hf-\phi\] where \(KE_{max}\) is the maximum kinetic energy of the emitted electrons, \(h\) is Planck's constant, \(f\) is the frequency of the incoming photons, and \(\phi\) is the work function, which represents the minimum energy required for an electron to escape from the material surface.

3. Connecting Planck's Hypothesis with Einstein's Theory of the Photoelectric Effect

Einstein used Planck's quantum hypothesis to explain the experimental observations of the photoelectric effect, which were inconsistent with classical physics. By proposing that light consists of discrete packets of energy called photons, and that the energy of these photons is quantized according to Planck's hypothesis, Einstein was able to develop a theory that explained the dependence of the emitted electrons' energy on the frequency of the incoming light, not its intensity. In summary, Einstein's theory of the photoelectric effect built upon Planck's quantum hypothesis by applying it to the interaction of light with matter, thus providing the first significant application of the quantum theory.