Data processing and calculation
Below is a raw data table showing the angles recorded for the position of each line detected.
In the experiment the hydrogen incident light was composed into three colors only
And the last line was observed to be more like blue-greenish colored
. The angles for the position of the colors found were recorded and their uncertainties were taken according to the smallest digit in the quantity.
In the forth column 2() was calculated as the following:
2() = R - L
And hence the uncertainty ±0.2 was calculated by adding the two uncertainties of the angles from the left and the right. In the last column the actual angle of each color position in the hydrogen spectrum was determined, and so is the uncertainty as follows
(max. value – min. value)/2 → [(2+0.2) -(2-0.2)]/2
The wavelength of each spectral line can be calculated using the diffraction grating equation:
= d sin ( )
Where d is the line spacing of the diffraction grating and in the experiment was
d= 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
The uncertainties of the wavelengths were calculated by taking the relative uncertainty of each value and adding them together. Example:
The uncertainty of sin ( ) for the color red = sin (22.9) = 0.389 is calculated as [sin(22.9+0.2) – sin(22.9-0.2)]/2 → ± 0.004
Thus, the relative uncertainty of d + relative uncertainty of sin ( ) = the relative uncertainty of the wavelength
x 649= 5.37 ±6nm wavelength uncertainty
To be able to compare the empirical measurements of the wavelength to the literature values, the percentage uncertainty of each wavelength need to be calculated;
(6/649) x100 = 0.92% uncertainty of red light
(6/426) x100= 1.41% uncertainty of violet
(6/476) x1001.27 % uncertainty of blue
From the wavelengths of each spectral line, Rydbergs constant can be determined empirically using Rydberg’s formula:
m and n are integers that identify the energy levels of the electron. For more explanation is that in order to emit light the hydrogen atom electron must make a transition between two orbits (from a higher energy level to a lower). m and n represent the quantum number of these energy levels where n is the initial energy level and m is the final one.
The Balmer series (only visible light is emitted) has a specific range of energy levels where m the final state electron state is equal to 2 and n has a quantum number of 3,4,5,6 each number correspond to a specific spectral line depending on their wavelength (the larger the integer the shorter the wavelength nred=3, nblue =4, nviolet=5 and nviolet=6).
Substituting this to Rydbergs formula:
n= 3,4,5,6
Processed Data2
Rydbergs constant was calculated by substituting each color wavelength in the formula with its energy levels number. When calculating R for the violet line, the quantum number that was taken into consideration as a substituent of n is n=6, because I thought a better result would be obtained for R and also for the reason that the wavelength of violet obtained was quite short if it would be compared to the accepted values of both the wavelengths of the violet in the Balmer series we find it that the empirical wavelength of violet is closer to the one with 410.2 nm. And this light wavelength(410.2nm) is obtained from the transition of a hydrogen electron from orbit number 6 to 2
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:
=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 =
The error is fairly simple and the calculated percentage uncertainty was quite bigger than the percentage error. So this makes the experiment successful.
