a) λ = 189.43 × 10⁻⁹ m b) λ = 269.19 × 10⁻⁹ m
Explanation: The expression that describes the diffraction network is
d sin θ= m λ
where m denotes the diffraction order.
Using trigonometry, we can determine the angle as follows:
tan θ = y / L
Since the diffraction spectrum is measured at minimal angles, tan θ simplifies to sin θ.
We replace with
d y / L = m λ
Using the first order where m = 1:
Now we need to find the line separation (d)
d = λ L / y
d = 501 × 10⁻⁹ × 9.95 × 10⁻² / 15 × 10⁻²
d = 332.33 × 10⁻⁹ m
Next, we find the wavelength of the other compound:
λ = d y / L
λ = 332.33 × 10⁻⁹ × 8.55 × 10⁻²/15 × 10⁻²
λ = 189.43 × 10⁻⁹ m
For Part B, the compound's wavelength is
λ = 332.33 × 10⁻⁹ × 12.15 × 10⁻² / 15 × 10⁻²
λ = 269.19 × 10⁻⁹ m.
