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Structure Of Atom

Question
CBSEENCH11005270

Give essential features of Bohr's model of atom.

Solution
In 1913, Neil Bohr proposed his model of the atom which was based on Planck’s quantum theory. The essential features of Bohr’s model of atom are:
1. An atom contains a heavy positively charged nucleus situated at the centre, with electrons revolving around the nucleus in fixed circular paths.

2. These circular paths are called orbits, shells energy levels or stationary states in which electron can revolve around the nucleus without emitting radiations. So far as an electron revolves in a certain orbit, its energy remains constant.

3. These different energy levels are designated by numbers 1, 2, 3, 4 etc. or letters K, L, M, N etc. starting from the nucleus. The greater the distance of the energy level from the nucleus more is the energy associated with it.

4. The electrons in an atom can revolve only in those orbits in which the angular momentum (mvr) of the electron is a whole number (n) multiple of a constant fraction numerator straight h over denominator 2 straight pi end fraction.
          mvr space equals space fraction numerator nh over denominator 2 straight pi end fraction space space or space space left parenthesis mv right parenthesis thin space left parenthesis 2 πr right parenthesis space equals space nh.
where m = mass of electron,
v = velocity of electron
r = radius of orbit.
h = Planck's constant,
n = whole number
This postulate indicates that the angular momentum of an electron moving in a circular orbit is quantisied. The angular momentum can be
fraction numerator straight h over denominator 2 straight pi end fraction comma space fraction numerator 2 straight h over denominator 2 straight pi end fraction comma space fraction numerator 3 straight h over denominator 2 straight pi end fraction comma space space.... fraction numerator nh over denominator 2 straight pi end fraction


5.  When an electron jumps from one stationary state to another, the difference of energy (∆E) between two states (E1 and E2) is emitted or absorbed, as radiation of frequency (v) given by the equation
∆E = E2- E1 = hv
If an electron jumps from higher energy state to a lower energy state, energy is emitted. Energy is absorbed by an electron when it jumps from a lower energy state to a higher energy state.
It is obvious that the electron cannot radiate energy if no energy level is available. That is why atoms do not collapse.
From Bohr model, one can calculate the energy En of an electron in an orbit n. This is given by the expression,


straight E subscript straight n space equals space fraction numerator negative 2.18 space cross times space 10 to the power of negative 8 end exponent straight J over denominator straight n squared end fraction space atom to the power of negative 1 end exponent
where space straight n space equals space 1 comma space 2 comma space 3.....
space space space space space space space space equals negative fraction numerator 13.595 space eV over denominator straight n squared end fraction atom to the power of negative 1 end exponent


Further, one can also calculate the radius of each circular orbit from the expression
rn = 0.529Å x n2 where n= 1,2,3......
The radius of the first orbit r1, called Bohr’s radius (n = 1) is 0.529A (or 52.9 pm).
Bohr model is also applicable to ions such as He+, Li2+ etc. For such cases,


                             straight E subscript straight n space equals space fraction numerator negative left parenthesis 13.595 space eV right parenthesis straight Z squared over denominator straight n squared end fraction atom to the power of negative 1 end exponent
and                      straight r subscript straight n space equals space fraction numerator 0.529 space straight Å space cross times space straight n squared over denominator straight Z end fraction
where Z is the atomic number and has values of 2 and 3 for He+ and Li2+ respectively.