3/24/2024 0 Comments Bohr's atom model![]() Thus, Bohr’s theory elegantly explains the line spectrum of hydrogen and hydrogenic species.īohr had calculated Rydberg constant from the above equation. The frequencies of the spectral lines calculated with the help of above equation are found to be in good agreement with the experimental values. The frequency of the photon of light thus emitted depends upon the energy difference of the two energy levels concerned (n1, n2) and is given by Since the life time of the electron in excited state is short, it returns to the ground state in one or more jumps.ĭuring each jump, energy is emitted in the form of a photon of light of definite wavelength or frequency. ![]() However, when an atom is subjected to electric discharge or high temperature, and electron in the atom may jump from the normal energy level, i.e., ground state to some higher energy level i.e, exited state. When n = ∞, E = 0, which corresponds to an ionized atom i.e., the electron and nucleus are infinitely separated.Įxplanation for hydrogen spectrum by Bohr’s theoryĪccording to the Bohr’s theory electron neither emits nor absorbs energy as long as it stays in a particular orbit. The lowest energy level of the atom corresponds to n=1, and as the quantum number increases, E becomes less negative. The energies are negative since the energy of the electron in the atom is less than the energy of a free electron (i.e., the electron is at infinite distance from the nucleus) which is taken as zero. Since this energy expression consist of so many fundamental constant, we are giving you the following simplified expressions. This expression shows that only certain energies are allowed to the electron. The total energy, E of the electron is the sum of kinetic energy and potential energy. Radius of nth orbit for an atom with atomic number Z is simply written as The radius of the smallest orbit (n=1) for hydrogen atom (Z=1) is ro. The greater the value of n, i.e., farther the energy level from the nucleus the greater is the radius. Hence only certain orbits whose radii are given by the above equation are available for the electron. Since the electrostatic force balance the centrifugal force, for the stable electron orbit.Īccording to Bohr’s postulate of angular momentum quantization, we have The centrifugal force acting on the electron is K = (where ∈o is permittivity of free space) r is the radius of the orbit in which electron is revolving.īy Coulomb’s Law, the electrostatic force of attraction between the moving electron Radius and Energy levels of hydrogen atomĬonsider an electron of mass ‘m’ and charge ‘e’ revolving around a nucleus of charge Ze (where, Z = atomic number and e is the charge of the proton) with a tangential Where E 2 and E 1 are the energies of the electron in the first and second energy levels, and ν is the frequency of radiation absorbed or emitted. Since the excited state is less stable, atom will lose it’s energy and come back to the ground state.Įnergy absorbed or released in an electron jump, (ΔE) is given by The quantum of energy absorbed is equal to the difference in energies of the two concerned levels. This new state of electron is called as excited state. If energy is supplied to an electron, it may jump (excite) instantaneously from lower energy (say 1) to higher energy level (say 2,3,4, etc.) by absorbing one or more quanta of energy. ![]() Such a stable state of the atom is called as ground state or normal state. Ordinarily an electron continues to move in a particular stationary state without losing energy. The different energy levels are numbered as 1,2,3,4, ( from nucleus onwards) or K,L,M,N etc. The greater the distance of the energy level from the nucleus, the more is the energy associated with it. Each stationary state is associated with a definite amount of energy and it is also known as energy levels. Hence these orbits are called stationary states. N = orbit number in which electron is presentĪs long as an electron is revolving in an orbit it neither loses nor gains energy. Of the finite number of circular orbits around the nucleus, an electron can revolve only in those orbits whose angular momentum (mvr) is an integral multiple of factor The force of attraction between the nucleus and an electron is equal to the centrifugal force of the moving electron. He applied quantum theory in considering the energy of an electron bound to the nucleus.Īn atom consists of a dense nucleus situated at the centre with the electron revolving around it in circular orbits without emitting any energy. Bohr developed a model for hydrogen atom and hydrogen like one–electron species (hydrogenic species). ![]()
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