# Purpose of the experiment

To determine the wavelength of the emission spectrum of Hydrogen.

# Theory

The set of frequencies emitted by each element is unique and can be used to identify that element.

The spectrograph in the lab uses a diffraction grating to separate spatially the wavelengths so that the different colors can be viewed at different angles. The angular location is given by the law:

Here *d* is the distance between two adjacent slits. For a diffraction grating with N rulings, the distance *d* is *d=1/N*. For example, in this lab *N=600* rulings per millimeter, so *d=1/600*. This value for *d* is in millimeter!

*m* is the order of the spectrum. If this is the first time you see the entire set (not just one color) of colors, that is *m=1*. In the other direction, *m* will be -1. If the Hydrogen cells in the lab are relatively new, students may see second order colors. This is when you see the set of colors (red, green, purple) for a second time. That will correspond to *m=2*.

#### Experimental Setup

The apparatus will be set up for you, but you will need to make sure it is aligned properly. Use the pictures below for guidelines.

You will be working with the Hydrogen emission spectrum. The three most pronounced wavelengths in the visible spectrum for H are: reddish (around 656 nm), bluish-green (around 496 nm) and violet (around 433 nm).

The diffraction grating has 600 lines per millimeter.

*Question: Determine the spacing between two adjacent slits, d?*

The central maximum should appear purplish-white. Turn the apparatus to the left and record the angles at which you see colors. This is the *m=1 *order. Turn the apparatus to the right and record the angles at which you see the same set of colors. This is the *m=-1* order. For each color, average the angle measured – it should be equal regardless of right or left. Then, use that angle to calculate the wavelength. Compare your results with the expected values (see the theory section).

# Experimental Data and Results

Use a spreadsheet to record your data. Calculate the wavelength of the visible colors and compare with their expected values: reddish (around 656 nm), bluish-green (around 496 nm) and violet (around 433 nm). Show your results to your instructor for a lab credit.

# Lab Assignment

Preserve your lab data until you learn about Quantum Mechanics, and the Hydrogen atom. Use the Bohr’s model of the Hydrogen atom to calculate the first three wavelengths for the Balmer series. Compare them to your lab results. Do they agree or disagree?