Question

Calculate the wavelength of light that has its second-order maximum at 45.0° when falling on a diffraction grating that has 5000 lines per centimeter.

Note: if there are 5,000 lines per cm, then the distance between lines (our value for d) is cm/5,000.
Select the correct answer
A. 707 nm
B. 629 nm
C. 654 nm
D. 749 nm
E. 788 nm

Answer 1

To find the wavelength of light with the second-order maximum at a 45.0° angle using a diffraction grating with 5000 lines per centimeter, we use the formula for diffraction maxima, solve for the wavelength, and obtain a result of 707 nm.

Step-by-step explanation:

To calculate the wavelength of light that has its second-order maximum at a 45.0° angle when utilizing a diffraction grating with 5000 lines per centimeter, we use the formula for diffraction maxima:

mλ = d sin(θ)

Where:

• m is the order of the maximum, which is 2 in this case (as it is the second-order maximum).
• λ is the wavelength of light we want to calculate.
• d is the distance between the lines in the grating.
• θ is the angle of the maximum, which is 45.0°.

First, let's find the value of d. As there are 5000 lines per centimeter:

d = 1 cm / 5000 lines = 1/5000 cm = 2×10⁻⁴ m

We plug our known values into the equation to find the wavelength:

2λ = 2×10⁻⁴ m × sin(45.0°)

Upon solving, we calculate λ:

λ = (2×10⁻⁴ m × sin(45.0°)) / 2

λ = 1×10⁻⁴ m × 0.7071

λ = 707.1×10⁻⁹ m

λ = 707.1 nm

Therefore, the wavelength of light is 707 nm.