Final answer:
The second-order Bragg angle for a crystal with a first-order angle of 12.1° is the angle for which sin(θ) is double that of sin(12.1°). However, the second-order angle itself is not simply double the first-order angle due to the non-linear relationship between angles and their sines.
Step-by-step explanation:
The student is asking about calculating the second-order Bragg angle given the first-order Bragg angle in a crystal. According to Bragg's law, nλ = 2d sin(θ), where n is the order of reflection, λ is the wavelength of the X-rays, d is the spacing between crystal planes, and θ is the Bragg angle.
To find the second-order angle, we would continue to use the same wavelength and spacing; therefore, as the order of reflection (n) is doubled from first to second order, the sine of the Bragg angle would also double. Thus, the second-order Bragg angle for a crystal with a first-order angle of 12.1° would be the angle θ for which sin(θ) is double that of sin(12.1°), within the domain where Bragg's law is applicable.
However, to calculate this angle accurately, we would use the relationship sin(θ₂) = 2 sin(θ₁) and solve for θ₂. We cannot assume the angle θ₁ itself is simply double the first-order angle, as this would be misleading due to the non-linear relationship between the angle and its sine.