quantization of atom in physics

quantization of atom

quantization of atom: According to Rutherford in 1910, atom which is positively charged at the nucleus and negatively charged at the obits would collapse in about 10-10s due attractive force between the nucleus and electrons, but in 1913 Niels Bohr  applied quantum theory to the problem and made a suggestion that electrons in atom is in discrete ( quantization ) energy state . This theory was developed by Max Plank to explain the radiation curve from black body and he stated that energy of electrons was distinct values of energy (energy quantization) and electron could lose its energy only in well defined step. Therefore the energy of radiation is given by

En = nhf            Where n = 1, 2,3 …,  h = Plank’s constant and f = frequency.

Energy level in atomic  quantization

The energy level in atom can be given as

E0, E1, E2, E3, E4, ……………. This shows that no intermediate energy level is possible according to Bohr. The lowest energy level systems in this state are stable. If the atom absorb energy and the energy of the atom reach the energy of the next allowed value E1, we say that the atom is excited or in excited state. When an atom is in excited state, it is not stable, therefore it tries to lose its energy to be stable .The Energy lost when an excited atom come back to its ground state is radiated  in form of electromagnetic radiation, and the energy is given as

En – E0 = hfn  =hc/ λ n  where h = Plank’s constant,  c = speed of light  γ = wavelength

Excitation energy in energy quantization of atom

The energy required to raise an atom from its ground state to next immediate energy level E1 is called the excitation energy, and is given by

Ex= eVx where eV is excitation potential. So if the atom is in its most stable state E0, and absorb amount of energy eV, which just remove electron from atom completely from atom, then we say that the atom is in excited state.

Note that E= zero energy of the atom.

Spectra emission in energy quantization of atom

Spectra is a plural of spectrum, it means the range of frequencies of electromagnetic radiation and their respective wavelengths and photon energies. It can also be described as the part of electromagnetic radiations that are visible to human eyes.

There are two main type of spectra:

Emission spectra:  the wavelength, color and photon energy of the emission spectra solely depend on the source. The examples of emission spectra are

  1. Continous spectra, this is emitted by sun, a piece of heated iron in flame and other incandescent solid and liquid. The all wavelength here are found over range.
  2. Line spectra: These kinds of spectra are emitted by monatomic gas, such as, hydrogen. In line spectrum only certain lines are visible.
  3. Band spectra: it consists of series of band and they are emitted by gas or liquid such as, oxygen, carbon monoxide, blood or potassium permanganate.

Absorption spectra: If white light is passed through a gas the continuous spectrum is crossed by dark line which corresponds to the lines observed in the emission spectrum which involve transition to the ground state. This shows that the absorption has taken place by the gas which is always in ground state.

The absorption which occur by electron in the atom, absorbing the energy from incoming radiation, is re-radiated in all direction, thus the energy that was originally traveling in one direction spread out and when compared to the rest of spectrum the wavelength appear dark

The ways atom can absorb energy

  1. In a flame : inelastic collision of atoms with higher energy molecules can raise atom to high energy level.
  2. In discharge tube: Inelastic collision with bombarding electrons can raise the energy level of atom

iii. From photon : If the photon energy E = hf is sufficient to excite an atom, the photon will be absorbed by the atom. That excited when it return to ground state will emit the same wavelength as photon but equal in all direction, so the intensity of radiation to the direction of incident photon is reduced. A dark line is also seen , which has the same wavelength as that of absorbed photon.

The absorption of photons explains the dark line in the sun’s visible spectrum. The sun emitting continuous spectrum is crossed by dark absorption lines, which is sometime called Fraunhofer lines. These are due to absorption by the outer gaseous layers of sun and a study of such line gives the astronomer a method to determine the composition of sun.

 Frequency, Wavelength and Energy of emitted photon.

According to Bohr an atom can make a transition from one energy level to a lower energy level by  emitting photon with energy equal to the energy difference between the initial and final levels .For example , if Ei is initial energy after transition  and Ef is the final energy after transition.  Therefore it can be said that

hf = hc/λ = Ei -Ef

For example when, a krypton atom emits a photon of orange light with wavelength, λ = 606 x 10-10m, the photon energy = 2.05eV. And also sodium emit Yellow-orange light with wavelength of  (589.0 and 589.6) x 10-9m,  when they make transition from two closed excited levels.

Fluorescence:  If an atom absorbs photon, in ultra-violet region to reach an excited level and drop back to ground level and emits two more photons with a smaller energy and longer wavelength, the phenomenon is called Fluorescence.

Balmer series:  This is formula for finding the different wavelength of photons emitted, by atom when it drops from high energy level to lower energy level. It is give as

1/λ =R (1/22 – 1/n2) where R = Rydberg’s constant = 1.097 x 107m, n=1, 2, 3, 4,……….   λ = wavelength

The other series proposed by Lyman and Paschen in ultraviolent and infra-red region.

The energy  levels En of hydrogen atom are given by

En  = 13.6eV/n2, n =1, 2, 3,…………..

 

 

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