Dual Nature of Matter and Radiation
Wave Nature of Matter, Davisson and Germer Experiment
 The square root of frequency, (ν) of the spectral line of the characteristic Xray spectrum is directly proportional to the atomic number, Z of the target element.
 \tt \sqrt{V} \propto Z \ or \ \sqrt{V} = a(z  b)

For K series (Characteristic x ray spectrum)
\tt \sqrt{\frac{\nu_{1}}{\nu_{2}}} = \left(\frac{Z_{1}  1}{Z_{2}  1}\right) \Rightarrow \sqrt{\frac{\lambda_{1}}{\lambda_{2}}} = \left(\frac{Z_{1}  1}{Z_{2}  1}\right)  The intercept on Zaxis gives the screening constant ‘b’ and it is constant for all spectral lines in given series but varies with the series.
b = 1 for K series (K_{α}  K_{β}  K_{γ})
b = 7.4 for L series. 
The wave lengths of characteristics x rays is given by \tt \frac{1}{\lambda} = R\left(z  b\right)^{2}\left[\frac{1}{n_1^2}  \frac{1}{n_2^2}\right]
 \tt \frac{\lambda_{k\alpha}}{\lambda_{k\beta}} = \frac{32}{27} , Ratio of k_{α} and k_{β} lines
 DAVISSON AND GERMER'S ELECTRON DIFFRACTION EXPERIMENT gives the evidence of matter wave existence.
 A beam of electron emitted by electron gun is made to fall on mickel crystal and along cubical axis at a particular angle
 Ni crystal behaves like a 3 dimensional diffraction grating and it diffracts the electron beam obtained from electron gun.
 The diffracted beam of electron received by the detector which can be positioned at any angle by rotating about the point of incidence.
 The energy of the incident beam of electron can also be varied by changing the applied voltage to the electron gun.
 Intensity of scattered beam of electrons was different at different angles of scattering.
 Intensity bump is maximum for 54 V potential and 50° scattering angle.
View the Topic in this video From 00:19 To 09:24
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1. The wavelength associated with a moving particle is known as de Broglie wavelength and it is given by
\lambda = \frac{h}{p} = \frac{h}{mv}
2. KE = \frac{P^{2}}{2m} \Rightarrow \lambda = \frac{h}{\sqrt{2 m \ KE}}
3. De Broglie wavelength associated with charged particles
For electrons (m_{c} = 9.1 × 10^{−31} kg):
\lambda = \frac{h}{\sqrt{2mqV}}
4. De Broglie wavelength associated with uncharged particles
For neutrons (m_{n} = 1.67 × 10^{−27} kg):
\lambda = \frac{h}{\sqrt{2mE}} = \frac{6.62 \times 10^{34}}{\sqrt{2 \times 1.67 \times 10^{27}E}}
5. de Broglie wavelength & wave nature
\lambda = \frac{h}{mv} = \frac{6.63 \times 10^{34}}{(0.046)(30)} = 4.8 \times 10^{34} m
6.The de Broglie wavelength λ associated with electrons using, for V = 54 V is given by davission & German Experiment
\tt \lambda = h/p = \frac{1.227}{\sqrt{V}}nm