Question

The first order diffraction X – rays from a certain set of the crystals and planes occurs at an angle of the 11.80 from the planes. If the planes are 0.281nm apart, the wavelength of the X = rays is (sin11.80 = 0.2045)

Answer 1

Hint
Here in the given question we have to find the wavelength of the X – rays
So for finding this we can simply use the formula
This formula is also known as bragg’s law-
 $ n\lambda = 2d\sin \theta $

Complete step by step answer
In the question it is given that -
Order of diffraction $ n = 1 $ ,
Distance between the planes $ (d) = 0.281 nm $ ,
As it is given in the nanometer so to convert it into the meter
$\Rightarrow 1 meter = 10^{-9} $ nanometer
Hence d = 0.281 $ \times $ 10-9 meter
Angle $ \theta $ = 11.80
For finding the wavelength
$\Rightarrow n\lambda = 2d\sin \theta $ $ n\lambda = 2d\sin \theta $
Here $ \lambda $ = It gives the value of the wavelength
So on simplification of the equation
$\Rightarrow \lambda = \dfrac{{2d\sin \theta }}{n} $
Hence putting the value in the equation
$\Rightarrow \lambda = $ $ \dfrac{{2 \times 0.281 \times {{10}^{ - 9}} \times {{\sin }^{}}({{11.8}^0})}}{1} $
And it is given that
 $\Rightarrow \sin ({11.8^0}) $ = 0.2045
So
$\Rightarrow \lambda = $ $ \dfrac{{2 \times 0.281 \times {{10}^{ - 9}} \times 0.2045}}{1} $
On solving the equation we get that
 $\Rightarrow \lambda = $ 0.1149 $ \times $ $ {10^{ - 9}} $ meter
 $\Rightarrow \lambda = $ 0.1149 nanometer
Hence the wavelength of the X – rays, $ \lambda = $ 0.1149 nanometer.

Note
Polarization is the attribute that wave oscillation have a definite direction relative to the direction of the wave .Em wave are the transverse wave that may be polarized The direction of the polarizations defined to be in the direction parallel to the electric field of the EM wave
Diffraction: It can be defined as the spreading of the wave around the obstacle. Diffraction takes place with sound; with electromagnetic radiation, such as the gamma rays X – rays and a very small moving particle like the atom, neutron