Problem 24 - Chemistry The Central Science

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.

Step-by-Step Solution

Answer

Planck's quantum hypothesis, introduced in 1900, states that energy is emitted and absorbed in discrete packets or quanta, formulated as \(E = h\nu\), where \(h\) is Planck's constant and \(\nu\) is the frequency. In 1905, Einstein used this hypothesis to explain the photoelectric effect by proposing that light is quantized into photons. When a photon with energy greater than the work function (\(\phi\)) of a metal incident on its surface, it transfers energy to an electron, causing it to be ejected. The maximum kinetic energy of the ejected electron is related to Planck's hypothesis through \(K_{max} = h\nu - \phi\).

Step 1: Understand the Planck's Quantum Hypothesis

Max Planck, in 1900, came up with his quantum hypothesis, while trying to find a mathematical formula to accurately describe the electromagnetic radiation emitted by a hot blackbody. Planck's quantum hypothesis can be summarized in the following statement: "Energy is not emitted continuously but is carried in discrete packets or quanta." Each quantum of energy can be expressed as the multiplication of a constant (Planck's constant, denoted by \(h\)) and the frequency (\(\nu\)) of the radiation: \[E = h\nu\]

Step 2: Learn about the Photoelectric Effect

The photoelectric effect is a phenomenon that occurs when light or electromagnetic radiation shines upon a metallic surface causing the emission of electrons. The emitted electrons are then called photoelectrons. The energy required to remove these electrons from the metal surface is termed as the work function.

Step 3: Understand Einstein's Theory of the Photoelectric Effect

In 1905, Einstein made use of Planck's quantum hypothesis to explain the photoelectric effect. According to Einstein, the photoelectric effect could only be explained if the incoming light was also quantized. He proposed that light consists of particles called photons that carry energy in discrete quanta. When a photon incident on a metal surface has energy equal to or greater than the work function of the metal, an electron is ejected.

Step 4: Relate Einstein's Theory with Planck's Hypothesis

Einstein proposed that when a single photon with energy \(E = h\nu\) is absorbed by an electron in a metal, the electron gains that energy. If the gained energy is equal to or greater than the work function (\(\phi\)) of the metal, the electron is ejected from the metal. The maximum kinetic energy of the ejected electron is given by the relation: \[K_{max} = E - \phi = h\nu - \phi\] To summarize: 1. Planck's quantum hypothesis introduced the concept of quanta that energy is emitted and absorbed in discrete packets. 2. Einstein applied this concept to explain the photoelectric effect by proposing that light is also quantized, and consists of particles called photons. 3. The photoelectric effect occurs when photons with energy greater than the work function of the metal incident on the metallic surface and transfer their energy to electrons, causing them to be ejected. 4. The maximum kinetic energy of the ejected electron can also be related to Planck's hypothesis through \(K_{max} = h\nu - \phi\).