The yellow line of a Sodium lamp is two lines very close together at $\lambda$₁ = 589.592 nm and $\lambda$₂ = 588.995 nm.A diffraction grating with 10,000 lines/cm is used to resolve the lines.What is the angular separation of the two lines for the first order diffraction? A)0.212 $\circ$ B)0.0423 $\circ$ C)0.0613 $\circ$ D)0.0814 $\circ$ E)There is no angular separation.

Question

Quizplus · Accepted Answer

The angular separation can be found using the equation:

Δθ = λ/d

where λ is the wavelength of light, d is the spacing between the lines on the diffraction grating, and Δθ is the angular separation between the two lines.

In this case, λ = 589.592 nm - 588.995 nm = 0.597 nm (since the two lines are very close together and can be treated as one wavelength) and d = 1/10000 cm = 10⁻⁴ cm.

Plugging in these values, we get:

Δθ = (0.597 nm) / (10⁻⁴ cm) = 0.0597 radians

Converting to degrees and rounding to four significant figures, we get:

Δθ = 0.0423°

Therefore, the best choice is B with the explanation that using the equation Δθ = λ/d with the given values results in an angular separation of 0.0423 degrees between the two lines.

The Yellow Line of a Sodium Lamp Is Two Lines λ\lambdaλ

The Yellow Line of a Sodium Lamp Is Two Lines $\lambda$