A diffraction grating has 8900 slits across 1.20 cm. If light with a wavelength of 500 nm is sent through it, how many orders (maxima) lie to one side of the central maximum?

The given data can be listed below,

• The number of slits in grating is, $N=8900$
• The distance of gratings is,$D=1.20\text{cm}$
• The wavelength of the line is, $\lambda =500\text{nm}$

According to Bragg's law, there is a clear correlation between the X-ray beam's wavelength, the separation between the crystal planes, and the angle at which it must strike the parallel atoms in a crystal for there to be strong reflection.

The distance between the slits is given by,

$d=\frac{D}{N}$

Here, Dis the distance of grating and Nis number of grating.

Substitute all the values in the above,

$$\begin{gathered} d=\frac{1.20\times {10}^{-2}\text{m}}{8900} \\ =1.348\times {10}^{-6}\text{m} \end{gathered}$$

The Bragg’s law for maximum order is given by,

$d\sin \theta =m_{\max }\lambda$

Here, d is the distance between slits,$\theta$ is the maximum diffraction angle,$\lambda$ is the wavelength of the light.

Substitute all the values in the above,

$$\begin{gathered} d\left(\sin 90°\right)=m_{\max }\left(500\times {10}^{-9}\text{m}\right) \\ {m}_{\max }=\frac{1.348\times {10}^{-6}\text{m}}{500\times {10}^{-9}\text{m}} \\ =2.69 \\ \approx 2 \end{gathered}$$

Thus, the maximum order of diffraction is 2.