Page 37 - 11-chem-5
P. 37
5.ATOMIC STRUCTURE eLearn.Punjab
This equation is derived as follows.
According to Planck’s equation
E = hv ........................
According to Einstein’s mass energy relationship
E = mc2 ........................ (29)
Where ’m’ is the mass of the material particle which has to convert itself into a photon; ‘and c’
is the velocity of photon. Equating two values of energy;
hv=mc2
Since
v= c
l
So, hc = mc2 or l= h ........................ (30)
l mc
According to equation (30), the wavelength of photon is inversely proportional to the momentum of
photon. Considering that nature is symmetrical, we apply this equation (30) to the moving electron
of mass’m’ and velocity V. This idea gives us the de-Broglie’s equation (28)
l= h ........................ (28)
mv
According to equation (28), the wavelength of electron is inversely proportional to momentum
of electron. Now, consider an electron which is moving with a velocity of 2.188x106 ms-1 in the first
orbit of Bohr’s model of hydrogen atom. Then, wavelength associating with it, can be calculated
with the help of equation(28)
h = 6.626x10-34 Js
me = 9.108x10-31 kg
l = 9.108 × 6.626 ×10-34 Js 106 ms-1 Since (J = kg m2 s-2 )
10-31kg ×2.188 ×
l =0.33x10-9m (10-9m=1mm)
l =0.33 nm
This value of wavelength (l)of electron while moving in the first orbit of H-atom is comparable
to the wavelength of X-rays and can be measured.
37
