Final answer:
The angle for the second-order maximum can be found using the equation sin(θm) = mλ/d. By plugging in the values provided and using a calculator, the angle is found to be approximately 40.0°.
Step-by-step explanation:
The angle at which a diffraction grating produces a second-order maximum can be found using the equation: sin(θm) = mλ/d, where θm is the angle, m is the order of the maximum, λ is the wavelength of light, and d is the spacing between the lines on the grating.
Since the first-order maximum occurs at 20.0°, we can use this information to find the angle for the second-order maximum. Let's assume that the wavelength of light is the same for both orders. Plugging in the values, we get: sin(θ2) = 2 * sin(θ1) = 2 * sin(20.0°). Using a calculator, we find that the angle for the second-order maximum is approximately 40.0°. Therefore, the correct answer is option a) 40.0°.