BOHR’S MODEL OF HYDROGEN ATOM
Ruther ford atomic model had certain drawbacks. Ruther ford failed to explain the following:
- How and where the electrons are arranged.
- Why Electrons do not fall into the nucleus.
- The line spectrum of hydrogen.
To answer these questions Bohr made the following assumptions.
- The electron is hydrogen atoms moves around the nucleus in any one the fixed orbits denoted by n= 1,2,3 or k, L, M.
- An electron does not radiate energy as long as it remains in the orbit.
- Electron loses energy when it jumps from higher to lower orbit and absorbs when jumps form lower to higher one. The energy difference between two levels is given by:
= 
- The angular momentum of electron can only be a whole number multiple of h/2p. Angular momentum of an electron is given by:
CALCULATION OF BOHR’S RADIUS: -
Hydrogen atom is considered as a circular body containing one electron and one proton. Proton is 1836 times heavier then electron and is considered to be static and at rest in the nucleus in a circular orbit, on shown in fig:
Any thing revolving in a circular path will be kept in the circle by the centripetal force. The centripetal force in given by the equation:
 ---------------- (1)
In case of atom, the columbic force of attraction is responsible for keeping the electron in the circular path. This columbic force is given by:
 (2)
In equation (2) Q1 is the charge on the nucleus for a simple hydrogen atom. The charge can simply be represented by ”e” but for atom with more than one proton, the charge can be represented by ”Ze”. Where Q2 is the charge on electron. Which can be represented by ”e” as well, so we can write
That:
Also K can be replaced on
So we can say that
 (3)
As centripetal force here is in fact the columbic force of attraction, therefore:
 (4)
This equation (4) shows that velocity of an electron is inversely proportional to the radius of the circle path i.e.
When the radius of the orbit decreases, velocity will increase.
To eliminate velocity from equation 4 we will use the postulate of angular momentum of electron i-e:
Squaring both side
 ------------------(5)
Comparing equation (4) and (5)
 ----------------(6)
In equation 6 n, h, l , m and e are constant and can be separated so
 -------(7)
Putting values in equation 7 and calculating
Equation (7) can thus be written as
r = n2 = 0.529A0
Z
For hydrogen atom with atomic number of 1, radius of atom is different abits can be determined of value of n is known then far:
For n= 1
For n= 2
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