Bohr Models

Introduction

Subatomic particles

The Nucleus

It exists at the centre of an atom, containing entire positive charge and almost whole of mass. The electron revolve around the nucleus to form an atom. The nucleus consists of protons (+ve charge) and neutrons.

A proton has positive charge equal in magnitude to that of an electron
(+1.6 × 10^–19 C) and a mass equal to 1840 times that of an electron.
A neutron has no charge and mass is approximately equal to that of proton.
The number of protons in a nucleus of an atom is called as the atomic number (Z) of that atom. The number of protons plus neutrons (called as Nucleons) in a nucleus of an atom is called as mass number (A) of that atom.
a particular set of nucleons forming an atom is called as nuclide. It is represented as _ZX^A.
The nuclides having same number of protons (Z), but different number of nucleons (A) are called as isotopes.
The nuclide having same number of nucleons (A), but different number of protons (Z) are called as isobars.
The nuclide having same number of neutrons (A – Z) are called as isotones.

Rutherford’s picture of atom

He shot alpha -particles toward a piece of gold foil only a few atoms thick and gave following results:

Atoms had to contain massive point like centers of positively charge surrounded by a large volume of mostly empty space. positively charged region was called the nucleus. He reasoned that closer the path of the α- particles to the nucleus of the atom, greater the deflection it experiences and the α- particles which directly hit on the molecules would rebound back. The nucleus must be very small as compared to size of whole atom.

Quantum Theory: According to this theory, a body cannot emit or absorb energy in the form of radiation of continuous energy; energy can be taken up or given out as whole number multiples of a definite amount known as a quantum. Light is imagined to consist of a stream of particles called photons. It E is the energy of a photon; its quantum for a particular radiation of frequency v sec1 is given by quantum theory as

E = hv

where h is a universal constant known as planck’s constant; h = 6.626 × 10^-27 erg second or

6.626 × 10^-34 Joule second (Js).

According to quantum theory, a body can emit or absorbs either one quantum of energy (hv) or whole number multiples of this unit, 2hv, 3hv......... nhv.

Atomic Spectra: If a gas is heated, it emits light. When this emitted light is analyzed in a spectrometer, the spectra obtained consists of a series of well - defined sharp lines, each line corresponding to a definite wavelength or frequency. These line spectra are characteristic of atoms.

Spectral lines are associated with electronic transitions. Hydrogen atom contains only one electron and the spectrum is the simplest to analyze. The space between two lines represents the frequency range in which no radiation is emitted by the hydrogen atom. Lines observed in the atomic spectra of hydrogen are grouped into the several series called spectral series.

The wave number of any line of hydrogen atom can be represented as a difference of two terms by the formula.

where R is called Rydberg constant (as this was formulated by Rydberg) and n₁ and n₂ are integers (n₂ > n₁, n₁ > 0).

THE BOHR’S MODEL:

Bohr made use of Planck’s quantum theory and gave the following postulates.

(i) The electron in an atom has only certain definite stationary states of motion allowed to it, called as energy levels. Each energy level has a definite energy associated with it. In each of these energy levels, electrons move in circular orbit around the positive nucleus. As one moves away from the nucleus, the energy of the states increases.

(ii) These states of allowed electronic motion are those in which the angular momentum of an electron is an integral multiple of h/2p or one can say that the angular momentum of an electron is quantized.

Angular momentum = m v r = n (h/2 π)

Where m is the mass, v is the velocity, r is the radius of the orbit, h is Planck's constant and n is a positive integer.

(iii) When an electron jumps from higher energy state to the lower energy state, it emits radiations in form of photons or quanta. However, when an electron moves from lower energy state to a higher state, energy is absorbed, again in form of photons.

(iv) The energy of a photon emitted or absorbed is given by using Planck's relation (E = hv).

ΔE = E₂ – E₁ = h v.

E₁, E₂are energy values of inner and outer states.

Where h = Planck's constant and v = frequency of radiation emitted or absorbed.

Note:

Bohr's Model is applicable only to one-electron atoms like: He⁺, Li⁺⁺ apart from H-atom.

Using Bohr’s postulates we get: