Question

In Davisson-Germer experiment an electron beam of energy 75eV falls normally on the surface via crystal if the maxima of order I. Obtained at an angle 450 to the direction incident then the inter atomic distance in the lattice plane of the crystal will be:
A) 1.0A°
B) 1.56A°
C) 1.20A°
D) 0.83A°

Answer 1

Hint: Wave nature of material particle as predicted by De-Broglie was confirmed by Davisson and Germen experiment. The electrons beam is made to fall on the nickel screen to measure the intensity of beam of electrons at different angles of $\varphi$.
Thus, the formula for wavelength is given by:
$\theta ={\displaystyle \frac{1}{2}}({180}^0-\varphi )$ ($\varphi$ is the angle at which electron beam is deflected)
$n\lambda =2d\sin \theta$ ($\lambda$ is the wavelength, d is the distance between atomic planes, $\theta$ is the angle at which maximum intensity is obtained, n denotes the order of diffraction).

Complete step by step solution:
Let us first discuss the results obtained by Davisson and Germen experiment.
Few inferences were drawn from experiments performed by Davisson and Germen.
Intensity of scattering electrons depends upon the angle of scattering $\varphi$. Always a bump or kink occurs at $\varphi$=500, the angle which the scattered beam makes with the incident beam. The size of the bump becomes maximum when accelerating voltage becomes 540.
Now, we will calculate the inter atomic distance in the lattice plane.
Using the relation:
$n\lambda =2d\sin \theta$..............(1)
where $\lambda ={\displaystyle \frac{h}{\sqrt{V}}}$ (h is the planck's constant, V is the energy)
$\Rightarrow \lambda ={\displaystyle \frac{12.27}{\sqrt{75}}}$ = $1.4168$
On substituting the value of $\lambda$ in equation 1
$\Rightarrow 1.4168=2\times d\sin 45$(We have substituted the value of theta as 45)
$\Rightarrow 1.4168={\displaystyle \frac{2}{\sqrt{2}}}d$ (sin 45° is equal to one upon square root two)
$\Rightarrow 1.4168=1.4142d$
$\Rightarrow d={\displaystyle \frac{1.4168}{1.4142}}=1.0A°$ (On rearranging the terms)

Thus, option (A) correct.

Note: The Davisson and Germen experiment has the most useful application of electron microscope which is widely used in the study of crystal structures, used in industries for the study of structures of textile fibers, purification of oil, composition of paper, paints etc, used in medicines to study viruses, disease causing agents which cannot be observed under ordinary microscope.