4th Postulate

4th Postulate hydrogen spectrum

In other to modify one orbit to another, electron must either emit or absorb energy which is proportional to the distance between the two orbits. Introduction of light energy bring about photon with a wavelength given by hv = E2 – E1 , in the corresponding energy substitution will give the following formula

4

On the above equation, it is examine that the last equation is identical to Balmer equation. π, m, e, c, and h, is a numerical value that can be used to evaluate R constant, the evaluation often give result that accept closely with the determine experimental value of Rydberg constant. Proceeding from Bohr theory, in as much n1 can have values 1, 2, 3, 4, 5, ….etc., it provide that other line series should live in the hydrogen spectrum alongside with the Balmer series. Suddenly to the theory, discovery of other series has taken place, in the ultraviolet, infrared, and far infared region of the electromagnetic spectrum. All of this series discovered have a line with a wavelength that are given by Balmer equation if the right value of n1 and n2 are used.

Every of the line stand for a different between two possible atomic state. Each of this state match with the electron in the hydrogen atom in an orbit which the radius increase with the n quantum number. The smallest value of n allowed is 1, the reason for this, is that the electron is as close to the nucleus as possible, the system has it minimum energy value to be negative. This value of energy is called the ground state, and is the most stable state of hydrogen atom.

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When a hydrogen atom absorb radiation that it energy is equal to the difference between that n = 1 and some higher value of n, the atom get excited, the atom is said be in excited state. When atom is excited, it is in an unstable state, and they decay fast to ground state, but this don’t usually take place in just a step. For example, when electron is initially promoted to n = 3state, the decay can go directly to the ground state or, it will first decay to n = 2 and then before it finally decay to n = 1, which is the ground state. Just it shown in the line series of hydrogen atom, single n = 1 → 3 excitation may lead to three emission line, as n = 3 → 1, n = 3 → 2, and n = 2→ 1.

When the required energy is given to the atom to remove the electron completely, we will end up having electron and hydrogen ion. But if the two particle combine with each other (H+ + e → H), the electron may find itself in a state that fit to any value of n, lead to the emission of many lines.

Hydrogen spectrum line are arrange into different series, according to the value of n where the emission ends, or where the absorption begins. The first few series are name after the founder, first observed of the series, is the Balmer series, which lie mostly in the visible region of the spectrum. The Lyman line which are in ultraviolet, the remaining series lie in the infrared the line in every of the series cloud with each other as they move along the series limit that fit to ionization of the atom and is viewed from the starting of the continuum emission.

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line spectra of hydrogen atom

Bohr Theory give detail of the hydrogen atom in the following ways;

  1. When hydrogen atom get excited, the electron move to orbits with higher energy level.
  2. Upon the electron returning to the ground state, or more stable state, it emit a photon of energy that fit to the different between the orbits.

Returning of electron to the ground state can take place directly or indirectly, given photon or several photon. Each of the spectral series fit to transitions between higher orbits and those having a given n value. It is acceptable to refer to the integer n as a quantum number.

Bohr Theory can be applied with the same success to hydrogen-like atoms that is ion made up of only single electron (He, Li, etc). equation of the electron energy in the nth orbit of these ion in give

E

Where Z stand for atomic number.

ready the the remaining postulate; 1st Postulate of Bohr Theory, Bohr 2nd Postulate, 3rd Postulate

Or watch below of full tutorial video of Bohr postulate

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