A chemist identifies compounds by identifying bright lines in their spectra. She

Question

A chemist identifies compounds by identifying bright lines in their spectra. She does so by heating the compounds until they glow, sending the light through a diffraction grating, and measuring the positions of first-order spectral lines on a detector 15.0 cm behind the grating. Unfortunately, she has lost the card that gives the specifications of the grating. Fortunately, she has a known compound that she can use to calibrate the grating. She heats the known compound, which emits light at a wavelength of 431 nm, and observes a spectral line 9.95 cm from the center of the diffraction pattern. What is the wavelength emitted by compound A that have spectral line detected at position 8.55 cm? Express your answer with the appropriate units. What is the wavelength emitted by compound B that have spectral line detected at position and 12.15 cm? Express your answer with the appropriate units.

Explanation / Answer

Here ,

for the grating

as d * sin(theta) = m wavelength

theta = arctan(9.95/15) = 33.6 degree

Now , in the equation

d * sin(33.6) = 431 *10^-9

d = 7.797 *10^-7 m

part A) for the position at 8.55 m

theta = arctan(8.55/15) = 29.7 degree

d * sin(theta) = wavelength

wavelength = 7.797 *10^-7 * sin(29.7) = 3.86 *10^-7 m

the wavelength is 3.86 *10^-7 m

part b)

theta = arctan(12.15/15) = 39 degree

d * sin(theta) = wavelength

wavelength = 7.797 *10^-7 * sin(39) = 4.91 *10^-7 m

the wavelength is 4.91 *10^-7 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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