A transmission diffraction grating with 648 inchs /nun is used to study the line

Question

A transmission diffraction grating with 648 inchs /nun is used to study the line spec-trum of the light produced by a hydrogen discharge tube with setup shown below. The grating is 1.2 in from the source (a hole at the center of the meter stick). An observer sees the first-order red line at a distance and = 0.305197 in from the hole. The speed of light is 2.998 times 108 m/s and the Planck's constant is 6.626 times 10-34 J s. Calculate the wavelength of the red line in the hydrogen spectrum. Hint: Do not use the small angle approximation. Answer in units of m

Explanation / Answer

angle is   arctan(.305197 / 1.2) = 14.270 degrees

then using diff grating eqn

   wavelength = sin@ / N = sin14.270 / 648 = 0.000380 mm = 3.80 x 10^-7 m

Note: this wavelength is nowhere near that of red light, but this is how the calculation comes out.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.