Question

1. A diffraction grating with 5.000 x 103 lines/cm is used to examine the sodium

Answer 1

Answer:

0.0002°, 0.1691°, 0.338°

Explanation:

Difference between the two line = 5.97 * 10-⁸m

d = 1 / N

N = 5.0 * 10³

d = 2.0 * 10⁴m

nL = Nsin¤

For first order

588.995 * 10-⁹ = 2.0 * 10-⁴ sin ¤

Sin¤ = 2.944*10-³

¤ = sin-¹ 0.002944

¤ = 0.1687°

First order ¤ =

Sin-¹(589.592*-⁹ / 2.0 * 10-⁴)

Sin-¹ (0.002947) = 0.1689°

Angular separation = 0.1689 - 0.1687 = 0.0002°

Second order ¤ = sin-¹ [2 (589.59*10-⁹ / 2.0*10-⁴)] = sin-¹ (0.005895)

Second order ¤ = 0.3378°

Angular difference = 0.3378° - 0.1687° = 0.1691°

Third order ¤ = sin-¹ [3(589.59*10-⁹ /2.0*10-⁴] = 0.5067°

Angular difference = 0.5067° - 0.1687° = 0.338°

Answer 2

d = 1 / N
N = 5.0 * 10³ / cm = 5.0 * 10⁵ / m
d = 2.0 * 10⁻⁶ m
nλ = d sinθ
θ = sin⁻¹(nλ / d)
First order θ₁ = sin⁻¹(588.995*10⁻⁹m / 2.0*10⁻⁶m) = sin⁻¹ (0.2945) = 17.13°
First order θ₂ = Sin⁻¹(589.592*10⁻⁹ / 2.0 * 10⁻⁶) = Sin⁻¹ (0.2948) = 17.14°
Angular separation = θ₂ - θ₁ = 17.14° - 17.11° = 0.01°
Second order θ₁ = sin⁻¹ [2(588.995*10⁻⁹ / 2.0*10⁻⁶)] = sin⁻¹ (0.5890) = 36.08°
Second order θ₂ = sin⁻¹ [2(589.592*10⁻⁹ / 2.0*10⁻⁶)] = 36.13°
Angular difference = 36.13° - 36.08° = 0.05°
Third order θ₁ = sin⁻¹ [3(588.995*10⁻⁹ /2.0*10⁻⁶] = 62.07°
Third order θ₂ = sin⁻¹ [3(589.592*10⁻⁹ /2.0*10⁻⁶] = 62.18°
Angular difference = 62.19° - 62.07° = 0.12°