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HYdrogen spectrum

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Introduction

Physics Lab Report

Hydrogen spectrum

Name: Mena Nadum

Class: IB07

Introduction

A hydrogen discharge tube is a device that can trap small amount hydrogen in a sealed tube of glass, and if potential difference is applied to that tube an emission of an atomic spectrum can be produced. The emission of the spectrum is produced from the excitation of the hydrogen electron (by the voltage) to a higher energy level and falling back to its original one.  In this practical a diffraction grating is used to analyze the emitted light into spectral Balmer (visible) lines. Using a spectrometer the wave length of each line can be determine and hence an experimental Rydbergs constant.

Apparatus

Hydrogen lamp

Diffraction grating

Spectrometer

Voltage power supply

Method

At the beginning of the experiment the slit of the collimator was adjusted to get a sharp focused light. The hydrogen lamp was placed in front of the slit. Then the diffraction grating was put at a right angle to the collimator. After the diffraction grating has analyzed the spectrum emitted, visible light was detected and spectral lines were produced at deferent angles.

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Middle

(max. value – min. value)/2 → [(2image00.png+0.2) -(2image00.png-0.2)]/2

The wavelength of each spectral line can be calculated using the diffraction grating equation:

image01.png= d sin ( image00.png)

Where d is the line spacing of the diffraction grating and in the experiment was

d= image02.png so its 1666.67nm

Since d value wasn’t measured in the experiment no uncertainties for it have been recorded. So  I found that it’s best to figure out an uncertainty to d by taking the last digit and get an uncertainty of ±0.01 nm.

Processed data1

Colors produced by the spectrum

Angle

image00.png/degree

±0.2º

Wavelength

image01.png/nm

±6nm

Red

22.9

649

Violet

14.8

421

Blue

16.6

476

The uncertainties of the wavelengths were calculated by taking the relative uncertainty of each value and adding them together. Example:

The uncertainty of sin ( image00.png) for the color red = sin (22.9) = 0.389 is calculated as [sin(22.9+0.2) – sin(22.9-0.2)]/2 → image03.png± 0.004

Thus, the relative uncertainty of d + relative uncertainty of sin ( image00.png) = the relative uncertainty of the wavelength

image04.pngx 649=  5.37 image03.png ±6nm wavelength uncertainty

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Conclusion

The Balmer series:

        Red                        656.3 nm

        Blue                     486.1 nm

            Violet                         434.0 nm

        Violet                        410.2 nm

Estimating the uncertainty of R for each line was ignored since there would be an average R and its uncertainty can be calculated.

Average uncertainty of R was determined by taking (max. R value – min. R value)/2

Percentage average Uncertainty is then calculated:

image08.png=2.60%

Then the experimental R value was compared with the accepted value by calculating the percentage error:

Percentage error = [(experimental value – literature value)/ literature value] x100

Percentage error =image09.png

The error is fairly simple and the calculated percentage uncertainty was quite bigger than the percentage error. So this makes the experiment successful.

...read more.

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