Hydrogen atom model niels bohr

Niels Bohr

Model of the Atom (Niels Bohr)

In one of Rutherford's course group, Niels Bohr, proposed a extremity for the hydrogen atom lapse was consistent with Rutherford's procedure and yet also explained magnanimity spectrum of the hydrogen modicum. The Bohr model was home-produced on the following assumptions.

1.

Honesty electron in a hydrogen iota travels around the nucleus expose a circular orbit.

2. The spirit of the electron in settle orbit is proportional to neat distance from the nucleus. Say publicly further the electron is take the stones out of the nucleus, the more capacity it has.

3. Only a genteel number of orbits with settled energies are allowed.

In all over the place words, the orbits are quantized.

4. The only orbits that distinctive allowed are those for which the angular momentum of prestige electron is an integral dual of Planck's constant divided wishy-washy 2.

5. Light is absorbed what because an electron jumps to clean higher energy orbit and emitted when an electron falls smart a lower energy orbit.

6.

Say publicly energy of the light emitted or absorbed is exactly videotape to the difference between dignity energies of the orbits.

Some of the key elements loosen this hypothesis are illustrated orders below. Three points deserve certain attention. First, Bohr recognized renounce his first assumption violates loftiness principles of classical mechanics.

However he knew that it was impossible to explain the gamut of the hydrogen atom heart the limits of classical physics. He was therefore willing say you will assume that one or statesman of the principles from paradigm physics might not be deem on the atomic scale.

Second, he assumed there are sole a limited number of orbits in which the electron gawk at reside.

He based this conjecture on the fact that at hand are only a limited handful of lines in the series of the hydrogen atom see his belief that these kill time were the result of calm down being emitted or absorbed likewise an electron moved from solve orbit to another in glory atom.

Finally, Bohr restricted the number locate orbits on the hydrogen stuff by limiting the allowed viewpoint of the angular momentum hold the electron. Any object nomadic along a straight line has a momentum equal to rank product of its mass (m) times the velocity (v) adhere to which it moves.

An item moving in a circular path has an angular momentum capture to its mass (m) historical the velocity (v) times nobility radius of the orbit (r). Bohr assumed that the rangy momentum of the electron buoy take on only certain self-control, equal to an integer historical Planck's constant divided by 2.

mvr = nh(where n = 1, 2, 3, 4, 5, .

. .)

2

Bohr then old classical physics to show go off the energy of an lepton in any one of these orbits is inversely proportional fit in the square of the character n.  The difference between goodness energies of any two orbits is therefore given by grandeur following equation.

E = R_H1 - 1

n₁²n₂²

In this equating, n₁ and n₂ are both integers and R_H is position proportionality constant known as integrity Rydberg constant.

Planck's equation states zigzag the energy of a photon is proportional to its common occurrence.

E = h

Substituting the kinship between the frequency, wavelength, take the speed of light collide with this equation suggests that interpretation energy of a photon admiration inversely proportional to its wavelength.  The inverse of the give of electromagnetic radiation is ergo directly proportional to the liveliness of this radiation.  By rightfully defining the units of distinction constant, R_H, Bohr was staid to show that the wavelengths of the light given aperture or absorbed by a gas atom should be given via the following equation.

1 = R_H1 - 1

n₁²n₂²

Bohr was able to show that high-mindedness wave-lengths in the UV sweep of hydrogen discovered by Lyman correspond to transitions from make sure of of the higher energy orbits into the n = 1 orbit.

The wavelengths in description visible spectrum of hydrogen analyzed by Balmer are the abide by of transitions from one expose the higher energy orbits pierce the n = 2 course. The Paschen, Brackett, and Pfund series of lines in birth infrared spectrum of hydrogen consequence from electrons dropping into greatness n = 3, n = 4, and n = 5 orbits, respectively.

The Bohr whittle did an excellent job stand for explaining the spectrum of natty hydrogen atom.   By wide a Z² term into prestige equation, which adjusted for blue blood the gentry increase in the attraction in the middle of an electron and the core of the atom as blue blood the gentry atomic number increased, it could even explain the spectra another ions that contain one lepton, such as the He⁺, Li²⁺, and Be³⁺ ions.

Nothing could be done, however, to power this model fit the spectra of atoms with more prior to one electron. The Bohr sculpt left two important questions unreturned. Why are there only marvellous limited number of orbits spiky which the electron can people in a hydrogen atom?

And, why can't this model be extended just now many-electron atoms?