Answer
Second order, m = 2.
Work Step by Step
An intensity maximum occurs when $d sin \theta=m \lambda$, where m is the order.
$$m=\frac{d sin \theta}{\lambda}$$
Find d from the information that there are 650 slits/mm.
$$d=\frac{1}{650000slits/m}=1.538\times10^{-6}m$$
The sine function cannot be greater than 1, so we should consider the longest visible wavelength when determining whether the order m can contain the entire visible spectrum.
Red light has wavelength of about 750 nm.
Find the maximum m at which is visible.
$$m_{max}=\frac{(1.538\times10^{-6}m)(1) }{750\times10^{-9}m }=2.05 $$
If m = 3, red light won’t be visible. So the largest m that contains the entire visible spectrum is the second order, m = 2.
