Final answer:
The angle at which the first-order maximum will form for 659-nm-wavelength green light on a diffraction grating with 2000 lines per centimetre is approximately 83.54 degrees.
Step-by-step explanation:
To find the angle at which the first-order maximum will form for 659-nm-wavelength green light, we can use the formula:
sin θ = (mλ) / d
where λ is the wavelength of the light, m is the order of the maximum, and d is the distance between adjacent lines on the diffraction grating. In this case, the diffraction grating has 2000 lines per centimetre, which means the distance between adjacent lines is 1/2000 cm. Plugging in the values, we get:
sin θ = (1 * 659 * 10-9) / (1 / 2000)
sin θ = 0.659 * 10-3 * 2000
sin θ = 1.318
Taking the arcsin of 1.318, we find that θ is approximately 83.54 degrees.