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Bohr's Model For Hydrogen Atom

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Bohr's Model For Hydrogen Atom - Lesson Summary

In 1913, Neils Bohr proposed an atomic model that quantitatively explained the structure of hydrogen atom and its spectrum.

It was based on the four postulates - Motion of electrons in an orbit, Fixed Energy of electrons, Transition of orbits by electrons, and Angular momentum of electrons.

Postulates:

1. The electron in the hydrogen atom can move around the nucleus in circular paths of fixed radius and energy called orbits also called stationary states. Electrons are held in orbits by an electrostatic force.

2. The energy of an electron in the orbit remains constant until the electron absorbs energy to jump to a higher orbit or releases energy to move to a lower orbit.

So each emission or absorption of radiation energy represents the electron transition from one stationery orbit to another.

The energy gap between the two orbits is given by equation

ΔE = E (final) - E (initial)

3. The frequency of the radiation emitted or absorbed can be represented by the equation,

v = ΔE/h = ( E2 - E1)/h

h is the Planck's constant.

4. An electron moving in a circular orbit has an angular momentum equal to the product of its mass (me), linear velocity (v) and radius of orbit (r), which can be expressed as

me × v × r = n × h/2π

n = 1, 2, 3...

The energy of a stationary state or orbit is given by the equation

En = - RH(1/n2)

where n is the principal quantum number of the orbit and RH is Rydberg's constant

Bohr's theory also applies to other hydrogen-like ions, such as He⁺, Li⁺² and Be. The energies of the stationary states of hydrogen-like ions are given by the expression

En = - 2.18 × 10-18 (Z2/n2) j

According to Bohr's model, electrons are held in orbits by virtue of an electrostatic force, so that doesn't fall into the nucleus. It quantitatively explains the emission and absorption line spectrums of hydrogen and hydrogen-like atoms.

Each spectral line in absorption or emission spectrum can be associated to transition of states by the electron of a particular hydrogen atom.

Bohr's model also shows that the intensity of each spectral line depends upon the frequency or wavelength of photons absorbed or emitted.

The frequency (v) associated with the absorption and emission of the photon and wave length(λ) can be calculated using the equation

v = ΔE/h =  R H h 1 n i 2 - 1 n f 2

λ = c/v

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