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 441 nm, and observes a spectral line 9.95 cm from the center of the diffraction pattern.

a) What is the wavelength emitted by compound A that have spectral line detected at position 8.55 cm?|

b)What is the wavelength emitted by compound B that have spectral line detected at position and 12.15 cm?

Answer 1

ans)

from above data that

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) = 441 *10^-9

d = 7.969 *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 = 7.969 *10^-7 * sin(29.7) = 3.95 *10^-7 m

the wavelength is 3.95 *10^-7 m

part b)

theta = arctan(12.15/15) = 39 degree

d * sin(theta) = wavelength

wavelength = 7.969 *10^-7 * sin(39) = 5.01 *10^-7 m

the wavelength is 5.01 *10^-7 m