Question

A diffraction grating with 2000 lines per centimeter is used to measure the wavelengths emitted by a hydrogen gas discharge tube.

(a) At what angles will you find the maxima of the two first-order blue lines of wavelengths 410 and 434 nm?
(b) The maxima of two other first-order lines are found at θ1=0.097rad and θ2=0.132rad. What are the wavelengths of these lines?

Answer 1

A diffraction grating can be used to find the angles of maximum intensity for different wavelengths of light. By using the formula sin(theta) = m * lambda / d, we can calculate the angles for the first-order blue lines with wavelengths of 410 nm and 434 nm. For the other first-order lines, we can rearrange the formula to solve for the wavelengths using the angles theta1 = 0.097 radians and theta2 = 0.132 radians.

Step-by-step explanation:

The diffraction grating can be used to find the angles of maximum intensity, or maxima, for different wavelengths of light. The formula to calculate the angle of a diffraction maximum is given by: sin(theta) = m * lambda / d, where theta is the angle of the maximum, m is the order of the maximum, lambda is the wavelength of the light, and d is the grating spacing.

(a) For the two first-order blue lines, we know the wavelength lambda = 410 nm and 434 nm. We can calculate the angles using the formula above. For the 410 nm line, m = 1 and d = 1/2000 cm. For the 434 nm line, m = 1 and d = 1/2000 cm. Plugging these values into the formula gives us the angles.

(b) For the two other first-order lines, we are given the angles theta1 = 0.097 radians and theta2 = 0.132 radians. We can rearrange the formula above to solve for lambda and then plug in the values of theta and d to find the wavelengths.