Diffraction grating equation for maximum intensity

Steps:

• Slit spacing d = 1 / (5000 lines/cm × 100 cm/m) = 1 / 5×10^5 m^{-1} = 2×10^{-6} m.
• For m=2, θ=30°, sin θ=0.5, so d sin θ = 2×10^{-6} × 0.5 = 1×10^{-6} m.
• Equation: d sin θ = m λ → 1×10^{-6} = 2 λ.
• λ = (1×10^{-6}) / 2 = 5×10^{-7} m.

Why D is correct:

• Matches λ from d sin θ = m λ, the standard grating formula for normal incidence.

Why the others are wrong:

• A: Twice D's value; error like using m=1 with doubled sin θ.
• B: Ten times D's value; likely forgot cm-to-m conversion, underestimating lines per m.
• C: Twice D's value; calculates for first-order (m=1) maximum.

Final answer: D