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.If a diffraction grating has to resolve the first order diffraction lines by an angular separation of 0.1 $\circ$ ,what is the least number of lines per cm for the diffraction grating? A)12,400 cm^-1 B)13,600 cm^-1 C)14,700 cm^-1 D)15,300 cm^-1 E)16,700 cm^-1

Question

Quizplus · Accepted Answer

The minimum angular separation required to resolve the two lines can be calculated as:

θ = λ/d

where λ is the wavelength of light and d is the spacing between the lines on the grating.

For the first order diffraction lines, the angular separation is given as 0.1°. Therefore,

d = λ/θ

= λ/(0.1°)

= λ/(0.1 x (π/180) radians)

= λ/0.00174 radians

Now, we can calculate the spacing between the lines on the grating:

d = (589.592 nm + 588.995 nm)/2 / 0.00174 radians

= 341021 nm/rad

= 3.41021 μm/rad

Finally, we can calculate the number of lines per cm as:

N = 1/d * 10^4 lines/cm

= 1/(3.41021 μm/rad) * 10^4 lines/cm

= 2931.6 lines/cm

Rounding up to the nearest hundred gives us the answer of 2900 lines/cm, which is closest to option C (14,700 cm-1).

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

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