Question

Which is the most reasonable slit spacing for a transmission diffraction grating?1) 0.001 nm2) 1000 nm3) 1 times 10^(–6) nm4) 1 times 10^6 nm

Answer 1

For the diffraction grating, the slits spacing should be comparable to the wavelength of length incident on the grating to observe the phenomenon of diffraction.

The wavelength of light considered for the for diffraction ranges from,

$\begin{gathered} 100\text{ nm to 10 }\mu m \\ or \\ 100\times10^{-9}\text{ m to 10}\times10^{-6}\text{ m} \\ or\text{ } \\ 1\times10^{-7}\text{ m or 1}\times10^{-5}\text{ m} \end{gathered}$

By simplifying the given value in meters,

$\begin{gathered} 1.\text{ 0.001 nm = 0.001}\times10^{-9}\text{ m = 1}\times10^{-12}\text{ m} \\ 2.\text{ 1000 nm = 1000}\times10^{-9}\text{ m} \\ =\text{ 1}\times10^{-6}\text{ m} \\ 3.\text{ 1}\times10^{-6}\text{ nm= 1}\times10^{-6}\times10^{-9}\text{ m} \\ =1\times10^{-15}\text{ m} \\ 4.\text{ 1}\times10^6\text{ nm= 1}\times10^6\times10^{-9}\text{ m} \\ =1\times10^{6-9}\text{ m} \\ =1\times10^{-3}\text{ m} \end{gathered}$

As the value of 1000 nm fall in this range and thus, considered as most reasonable slit spacing.

Hence, option 2 (1000 nm) is the correct answer.