Posted: October 24th, 2022

Conceptual Physics II

Introduction
On this lab, you’ll examine how a grating spectrometer works to measure the seen spectrum of the hydrogen atom, together with another components. As we mentioned in lecture, a spectrometer is an instrument used for measuring the wavelength (or frequency) of electromagnetic radiation. It consists of a number of components, the principle ones being a slit, a dispersive ingredient like a prism, and a detector of the radiation. The slit clearly defines the supply of the radiation, the dispersive ingredient divides the radiation into its part frequencies/wavelengths primarily based on their angle of refraction, and eventually the detector detects the radiation.
One of many spectra that you’ll research at the moment is the emission spectrum emitted by the hydrogen atom. This explicit spectrum known as the Balmer Sequence. The Balmer sequence is the identify given to a sequence of spectral emission traces of the hydrogen atom that consequence from electron transitions from larger ranges right down to the vitality stage with principal quantum quantity 2, like proven within the diagram under:

The Balmer Sequence is given by the Rydberg components. This components can be utilized to calculate the reciprocals of the wavelengths within the sequence. Particularly:
Components 1
Right here, R known as the Rydberg fixed and has a price , whereas n takes on integer values starting with three. There are sometimes three or 4 traces seen within the Balmer Sequence, similar to the three or 4 transitions that excited electrons could make as they transfer from the next to a decrease vitality state within the Hydrogen atom. n =1 corresponds to the bottom vitality state out there within the Hydrogen atom, and every subsequent worth of n corresponds to the following out there vitality stage within the atom.
When an electron within the Hydrogen atom has been excited to the third vitality stage (n =three), it might make a transition to the bottom vitality stage, emitting a photon with frequency within the purple area. This reveals up as a purple line within the emission spectrum of Hydrogen and is named the Hydrogen-alpha line. The road similar to is inexperienced, and the final two traces seen, similar to and , respectively, are violet. Strains for values of n past 6 are within the ultraviolet and are usually not seen.
On this lab, you’ll first watch a video exhibiting the emission spectra of quite a lot of components after which use a simulator to measure the Balmer spectrum of Hydrogen. You’ll then evaluate your measured values to these computed from the Rydberg components.

Process

Half I

1. Watch the next quick video, which reveals the emission spectra of various components, in addition to a thermal emitter, as mild from every is handed by means of a diffraction grating: https://www.youtube.com/watch?v=2ZlhRChr_Bw

2. Now reply the next questions, primarily based on the video you simply watched:

• (four pts) What number of spectral traces present up within the emission spectrum of Hydrogen? What colours are they?

• (2 pts) Does the emission spectrum of Helium encompass fewer or extra spectral traces than Hydrogen?

• (2 pts) What number of spectral traces present up within the emission spectrum of Mercury? Are they the identical or totally different than the traces within the Hydrogen spectrum?

• (four pts) What do you discover in regards to the emission spectrum of Carbon Dioxide? (Trace: Carbon Dioxide is a molecule made up of two components; Carbon, and Oxygen. Would you anticipate to see roughly spectral traces within the spectrum of a molecule, as in comparison with these from a single ingredient like Carbon or Oxygen?)

• (four pts) Lastly, what do you discover in regards to the emission spectrum of a thermal emitter like an incandescent lamp? Why is that this spectrum totally different than that of a single ingredient?

Half II

Now that you’ve got a greater understanding of what the emission spectra of various components appear to be, let’s use a simulator to investigate the absorption spectrum of Hydrogen in a bit extra element.

1. Go to https://physics.bu.edu/~duffy/HTML5/emission_spectra.html and decide “Hydrogen”, just under the Emission Spectra picture. You need to see four spectral traces present up. These correspond to the 4 potential transitions (that fall within the seen a part of the spectrum) an electron could make within the Hydrogen atom.

2. (four pts) For every of the 4 spectral traces within the Hydrogen spectrum, report the corresponding wavelength within the “Measured” column within the desk under.

three. (12 pts) Calculate the wavelength of the primary 4 traces within the Balmer Sequence utilizing the Rydberg components (Equation 1) and report your ends in the “From Components 1” column within the desk. Don’t neglect to take the reciprocal of the wavelength because the final step in your calculations. Moreover, keep in mind to transform your reply from m to nm in order that it matches your measured values.
For reference, 1 nm = 1 x 10-9 m.
Present all calculations on a separate sheet of paper.

• (eight pts) Calculate the p.c distinction between every of your measurements and the worth calculated from the Rydberg components. (The p.c distinction reveals the deviation of the measured worth from the components worth and will be calculated by equation:

Components Wavelength – Measured Wavelength
_______________________________________ x 100 = % Distinction

Components Wavelength

Colour n Wavelength (nm)
Measured Wavelength (nm)
From Components 1 % Distinction
Crimson
three
Inexperienced
four
Violet 1
5
Violet 2
6

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