Bohr's Model of the Hydrogen Atom

The Bohr model of the hydrogen atom was the first atomic model to successfully explain the atomic hydrogen radiation spectra. Niels Bohr proposed the atomic Hydrogen model in 1913. The Bohr Model of the Hydrogen Atom attempts to fill in some of the gaps left by Rutherford's model. It has a special place in history because it introduced the quantum theory, which gave rise to quantum mechanics.

In comparison to the valence shell atom model, the Bohr model is a more rudimentary representation of the hydrogen atom. It may be determined as a first-order approximation of the hydrogen atom using the broader and far more precise quantum mechanics, and hence may be regarded as an obsolete scientific theory. Arthur Erich Haas suggested an analogous quantum model in 1910, but it was rejected until the 1911 Solvay Congress. The old quantum theory refers to the quantum theory that existed between Planck's discovery of the quantum (1900) and the introduction of mature quantum mechanics (1925).

Planetary Model of the Atom

Quantum mechanics first appeared in the mid-1920s. One of the founders of quantum mechanics, Neil Bohr, was interested in a hotly debated topic at the time – the structure of the atom. Numerous atomic models had emerged, including J.J. Thompson's theory and Ernest Rutherford's discovery of the nucleus. However, Bohr supported the planetary model, which stated that electrons revolved around a positively charged nucleus in the same way that planets revolved around the sun.

Bohr model of hydrogen atom postulates

1. An atom, such as a hydrogen atom, has numerous stable circular orbitals in which an electron can remain.
2. An electron remains in a specific orbit in which no energy is emitted or absorbed.
3. When an electron may jump from one orbit to another with more energy absorption but from one orbit to another with lower energy emission.
4. An electron's angular momentum in an orbit is an integral multiple of h/2π. This integral multiple is known as the hydrogen atom's primary quantum energy level. As a result, mvr = nh/2π, where m = electron mass, v = electron tangential velocity, and r = radius of Bohr energy levels.

Atomic line spectra

Another example of quantization is atomic line spectra. When an element or ion is heated by a flame or excited by an electric current, the excited atoms emit light of a specific color. The emitted light can be refracted by a prism, resulting in spectra with a distinct striped appearance due to the emission of specific wavelengths of light. The wavelengths of some emission lines could even be fitted to mathematical equations in the relatively simple case of the hydrogen atom. The equations, however, did not explain why the hydrogen atom emitted those specific wavelengths of light. Prior to Bohr's model of the hydrogen atom, scientists were baffled as to why atomic emission spectra were quantized.

Bohr’s Equation

The Bohr Model of the Hydrogen Atom proposed the planetary model first, but an assumption about electrons was later made. The assumption was that the structure of atoms could be quantized. Bohr proposed that electrons orbited the nucleus in fixed-radius orbits or shells. Only shells with the radius specified by the equation below were permitted, and electrons could not exist between these shells. The equation gives the mathematical expression for the allowed value of the atomic radius.

r(n) = n² × r(1)

Where n is a positive integer and r(1) is the smallest radius allowed for the hydrogen atom, also known as the Bohr's radius. The radius of Bohr has the value: 

r(1) = 0.529 × 10^-10 m

By considering electrons in circular, quantized orbits, Bohr calculated the energy of an electron in the nth level of hydrogen as: 

E(n) = -(1/n²) × 13.6 eV

Where E is the lowest possible energy of a hydrogen electron and 13.6 eV is the lowest possible energy of a hydrogen electron E(1). The obtained energy is always a negative number, with the ground state n = 1 having the most negative value. The reason for this is that the energy of an electron in orbit is relative to the energy of an electron completely separated from its nucleus, n=infinity, which has an energy of 0 eV. Because an electron in a fixed orbit around the nucleus is more stable than an electron far from its nucleus, the energy of the electron in orbit is always negative.

Absorption and Emission: To be excited to a higher energy level, an electron would absorb energy in the form of photons, according to Bohr's model. The excited electron is less stable after escaping to a higher energy level, also known as the excited state, and would therefore rapidly emit a photon to return to a lower, more stable energy level. The energy difference between the two energy levels for a specific transition is equal to the energy of the emitted photon.

Limitations of the Bohr Model of the Hydrogen Atom:

1. It violates the Heisenberg Uncertainty Principle by treating electrons as having a known radius and orbit.
2. The Bohr Model calculates the ground state orbital angular momentum incorrectly.
3. It predicts the spectra of bigger atoms incorrectly.
4. The relative intensities of spectral lines are not predicted.
5. Fine and hyperfine structures in spectral lines are not explained by the Bohr Model.
6. It does not account for the Zeeman Effect.

Although the modern quantum mechanical model and the Bohr Model of the Hydrogen Atom appear to be diametrically opposed, the fundamental idea in both is the same. Classical physics cannot adequately describe all of the phenomena that occur at the atomic level. 

Bohr Model for Heavier Atoms

The nucleus of heavier atoms contains more protons than the nucleus of a hydrogen atom. To cancel out the positive charge of all of these protons, more electrons were necessary. Each electron orbit, according to Bohr, could only hold a certain amount of electrons. When the level was full, extra electrons were moved to the next level. Thus, for heavier atoms, the Bohr model explained electron shells. Some of the atomic features of heavier atoms were explained by the model, which had never been replicated before. 

For example, the shell model explained why atoms became smaller as they moved through a period (row) of the periodic table while having more protons and electrons. It also explained why noble gases were inert, as well as why atoms on the left side of the periodic table attract electrons while those on the right lose them. However, because the model assumed that electrons in the shells did not interact with one another, it was unable to explain why electrons appeared to stack in an irregular fashion.

Improvements to the Bohr Model

The Sommerfeld model, sometimes known as the Bohr-Sommerfeld model, was the most notable improvement to the Bohr model. Electrons in this scenario travel in elliptical orbits around the nucleus rather than circular orbits. The Sommerfeld model explained atomic spectral effects better, such as the Stark effect in spectral line splitting. The model, however, was unable to handle the magnetic quantum number. In 1925, the Bohr model and models based on it were supplanted by Wolfgang Pauli's quantum mechanics-based model. That model was modified to produce the present model, which Erwin Schrodinger introduced in 1926. Today, wave mechanics is used to describing atomic orbitals in order to understand the behavior of the hydrogen atom.

Discovery since Bohr's hydrogen model

The Bohr model did an excellent job of explaining the hydrogen atom and other single-electron systems like He⁺. Unfortunately, when applied to the spectra of more complex atoms, it did not perform as well. Furthermore, the Bohr model provided no explanation for why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field.

In the decades that followed, scientists such as Erwin Schrödinger demonstrated that electrons can be thought of as both waves and particles. This means that it is impossible to know both an electron's position in space and its velocity at the same time, as stated more precisely in Heisenberg's uncertainty principle. Bohr's idea of electrons existing in specific orbits with known velocity and radius is contradicted by the uncertainty principle. Instead, we can only calculate the chances of finding electrons in a specific region of space surrounding the nucleus.

The modern quantum mechanical model may appear to be a significant departure from the Bohr model, but the central idea remains the same: classical physics is insufficient to explain all phenomena at the atomic level. Bohr was the first to recognize this by incorporating the concept of quantization into the electronic structure of the hydrogen atom, allowing him to explain the emission spectra of hydrogen and other one-electron systems.

Sample Questions

Question 1: What are subatomic particles?

Answer:

Subatomic particles are the particles that make up an atom. Protons, electrons, and neutrons are all included in this category.

Question 2: What are the shortcomings of Bohr’s atomic model?

Answer: 

The structure of an atom, according to this atomic model, provides poor spectral predictions for larger atoms. It also failed to account for the Zeeman effect. It could only explain the hydrogen spectrum successfully.

Question 3: How can the total number of neutrons in the nucleus of a given isotope be determined?

Answer:

The total number of protons and neutrons in an isotope is used to calculate its mass number. The total number of protons in the nucleus is described by the atomic number. As a result, the number of neutrons is calculated by subtracting the atomic number from the mass number.

Question 4: How do the atomic structures of isotopes vary?

Answer:

They differ in terms of the total number of neutrons present in the atom's nucleus, as described by their nucleon numbers.

Question 5: What is the structure of an atom?

Answer:

Atoms are made up of protons, electrons, and neutrons. The protons (positively charged) and neutrons are found in the nucleus (centre) of an atom (without charge). The outermost regions of the atom are known as electron shells, and they contain (negatively charged) electrons.