Developments Leading to Bohr's Model of Atom

Neils Bohr, a scientist, expanded on Rutherford's model of the atom through his experiments. The dual nature of electromagnetic radiation was an important element in the development of Bohr's model. This indicates that radiations can have both wave-like and particle-like properties. Let's take a closer look at the evolution that led to Bohr's model of an atom.

Wave Nature of Electromagnetic Radiation

When electrically charged particles travel under acceleration, alternating magnetic and electrical fields are formed and communicated, according to James Maxwell's 1870 proposal. These fields are transferred in the form of waves and are referred to as electromagnetic waves or electromagnetic radiation. For many years, scientists have pondered the nature of light as a sort of radiation. Initially, scientists assumed that light was made up of particles called corpuscles. The wave nature of light was only discovered in the early nineteenth century. Maxwell was the first to demonstrate, using the notion of electromagnetic radiation, that electricity, magnetism, and light are all various manifestations of the same phenomena.

Properties of Electromagnetic Wave Motion

1. Oscillating charged particles generate perpendicular oscillating electric and magnetic fields. These fields are also perpendicular to the wave's propagation direction.
2. Electromagnetic waves, unlike sound or water waves, do not require a medium to propagate. They have the ability to travel across a vacuum.
3. There are many distinct types of electromagnetic radiations available today, each with a different wavelength or frequency. They are all part of an electromagnetic spectrum. The names and applications of the various parts of this spectrum vary. For example, the Infrared region around 1013 Hz is utilised for heating, and the UV component of the sun's rays is at 1016 Hz. Visible light is the little component around 1015 Hz, which our eyes can only see. Non-visible light detection necessitates the use of specialised equipment.

Electromagnetic Radiation Properties

• Frequency (v) - The number of waves passing through a specific place in one second. Hertz (Hz, s^-1) is the SI unit named after Heinrich Hertz.
• Wavelength (λ) - Wavelength is measured in the same units as length, which is the meter (m). However, because electromagnetic radiation is made up of multiple waves of small wavelengths, we utilise smaller units.
• Wavenumber: The number of wavelengths per unit length is referred to as the wavenumber. Its units are m^-1 which are the inverse of wavelength.
• The speed of light (c): It is the rate at which all types of electromagnetic radiation, regardless of wavelength, travel in a vacuum (3.0 x 10⁸ ms^-1). The equation: relates the wavelength, frequency, and speed of light.

c = ν λ

Particle Nature of Electromagnetic Radiation and Black-body Radiation

1. Although the wave nature of electromagnetic radiation explains phenomena such as "diffraction" and "interference," certain crucial properties remain unknown. The following observations are unexplained:
2. The nature of radiation emission from heated bodies is referred to as black-body radiation.
3. The photoelectric effect, or the emission of electrons from a metal surface when exposed to radiation.
4. The heat capacity of solids varies.
5. Atomic line spectra with reference to hydrogen.

When heated, solids emit radiations with a wide range of wavelengths in this phenomenon. The heating of an iron rod in a furnace or over a flame is the best example of this. It begins as a drab red colour and becomes brighter as the temperature rises. As the temperature rises, it becomes white, then blue. This simply means that as the temperature rises, the frequency of the emitted radiation rises from a lower to a higher frequency. The red colour is in the lower frequency region of the spectrum, while the blue colour is in the higher frequency zone. 

A black body is an ideal body that emits and absorbs all wavelengths of radiation. This type of radiation is known as black-body radiation. The frequency distribution of a black body's emitted radiation is solely determined by its temperature. The radiation intensity at a given temperature increases as the wavelength decreases reaches a maximum and then begins to drop as the wavelength decreases further.

Planck’s Quantum Theory and Explanation for Black-Body Radiation

The phenomena of black-body radiation and the photoelectric effect are not well explained by classical physics or the wave theory of light. Max Planck provided the first solid explanation for the phenomenon of black-body radiation in 1900. He proposed that atoms or molecules emit or absorb energy only in discrete amounts known as quantum amounts, rather than in a continuous fashion. The smallest amount of energy emitted or received in the form of electromagnetic radiation is referred to as a quantum.

Photoelectric Effect

Einstein used Planck's quantum theory to explain the photoelectric effect in 1905. According to Planck's quantum theory, firing a light beam on a metal surface is equivalent to shooting a beam of particles or photons at the metal. In this situation, when a sufficiently energetic photon collides with an electron in the metal, the photon quickly transmits its energy to the electron, and the electron is ejected without any time lag. A more intense light beam has a greater number of photons and hence ejects a greater number of electrons. Finally, the kinetic energy of the expelled electron increases as the energy carried by a photon increases. The kinetic energy of the expelled electron is thus proportional to the frequency of the electromagnetic radiation. 

Dual Behavior Of Electromagnetic Radiation

The photoelectric effect and black-body radiation are explained by the particle nature of light. Interference and diffraction, on the other hand, are explained by the wave nature of light. This disparity presented scientists with a quandary. Finally, they agreed that light has both wave-like and particle-like features, implying that it has dual behaviour. When light propagates, it has wave-like properties, whereas when it interacts with matter, it has particle-like properties.

Sample Questions 

Question 1: If the kinetic energy of an electron is increased four times, the wavelength of the de-Broglie wave associated with it would become how many times of itself?

Answer:

The wavelength has an inverse relationship with the square root of the kinetic energy. As a result, if KE is increased four times, the wavelength is cut in half.

Question 2: Name the scientist who first formulated the atomic structure.    

Answer:

In 1808, a British teacher named John Dalton proposed the atomic structure. He originally proposed a solid scientific foundation known as Dalton's atomic hypothesis.

Question 3: Why Rutherford’s model could not explain the stability of an atom?  

Answer:

When charged particles are accelerated, they should create electromagnetic radiation, according to Maxwell's electromagnetic theory. As a result, an electron in an orbit will emit radiation indefinitely; the orbit will then continue to shrink, which is not the situation in an atom.

Question 4: How does the intensity of light affect photoelectrons?    

Answer:

The quantity of electrons ejected and the kinetic energy associated with them is proportional to the intensity of light directed at the metal.

Question 5: What did Einstein explain about the photoelectric effect?

Answer:

In 1905, Einstein used Planck's quantum theory of electromagnetic radiation to explain the photoelectric effect. Energy in each quantum of light is equal to a constant multiplied with the speed of light.