Answer:
The order of maximum is
![n = 5](https://img.qammunity.org/2021/formulas/mathematics/college/pwyq5dqls15ocbaouicnk7qc83zmdzghxo.png)
Step-by-step explanation:
From the question we are told that
The diffraction grating is k = 300 lines per mm = 300000 lines per m
The wavelength is
![\lambda = 630 \ nm = 630 *10^(-9) \ m](https://img.qammunity.org/2021/formulas/physics/college/xpdlav58wne4gsxkgjqowghjwnerfijldx.png)
Generally the condition for constructive interference is mathematically represented as
![dsin \theta = n * \lambda](https://img.qammunity.org/2021/formulas/physics/college/w9inuxrdnhabsb4oml2beaoap3081ppjwq.png)
Here n is the order maximum
d is the distance the grating which is mathematically represented as
![d = (1)/(k)](https://img.qammunity.org/2021/formulas/physics/college/sgu7w4l45846txjmmal6fon3f3fbtcbhpb.png)
=>
![d = (1)/(300000)](https://img.qammunity.org/2021/formulas/physics/college/s7necubk0wyowxvwa519c78c1f7x6v69vh.png)
=>
So
![n = (dsin \theta)/( \lambda)](https://img.qammunity.org/2021/formulas/physics/college/t2wwik2u4aofxjhw5iabbeg0vox1lvon5p.png)
at maximum
![sin\theta = 1](https://img.qammunity.org/2021/formulas/physics/college/fu9edxhb66hhpcd1720kybl8rk7agbpqxi.png)
![n = (d)/(\lambda)](https://img.qammunity.org/2021/formulas/physics/college/ki2y4ah4ue4gzsc5y6t435bo0tiymhflz6.png)
=>
=>
![n = 5](https://img.qammunity.org/2021/formulas/mathematics/college/pwyq5dqls15ocbaouicnk7qc83zmdzghxo.png)