# Wave Nature of Matter, Davisson and Germer Experiment

• The square root of frequency, (ν) of the spectral line of the characteristic X-ray 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 Z-axis 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 (Kα | Kβ | Kγ)
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 kα and kβ 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 (mc = 9.1 × 10−31 kg):
\lambda = \frac{h}{\sqrt{2mqV}}

4. De Broglie wavelength associated with uncharged particles
For neutrons (mn = 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