Diffraction grating equation: d sinθ = mλ

Steps:

• Calculate slit spacing d: 5000 lines/cm = 5×10^5 lines/m, so d = 1/(5×10^5) = 2×10^{-6} m.
• Use formula d sinθ = mλ with m=2, θ=30° (sin30°=0.5).
• Substitute: λ = (d sinθ)/m = (2×10^{-6} × 0.5)/2 = (1×10^{-6})/2 = 5×10^{-7} m.
• Matches option B.

Why B is correct:

• It equals λ from d sinθ = mλ, the grating equation for constructive interference maxima.

Why the others are wrong:

• A: Half of calculated λ, likely from using m=4 or sinθ=0.25.
• C: Twice calculated λ, from forgetting to divide by m=2.
• D: Duplicate of B, not a distinct wrong option.

Final answer: B