Question

DATA ANALYSIS Line Color Krown He Wavelength Experimental Spectrometer Value 3889 nm 4.5 Blue 468.6 nm 501.6 nm Yellow 5876 nm 5.6 I 5.8 Orange 6678 nm Red 706 5 nm Name of Gas Line Color Spectroscope Literature avelength (nm) Corrected Wavelength W Percent Error (%) Reading inm hydrogen Red 6.00 G502 Volet S. & 416.15 Red 6.5 706.5 violet 4.5 /388.9 Atomic Spectra

Answer 1

ANSWER:

1) Step 1: calibration curve

• The first step is plot the Experimental spectrometer value vs. known wavelength, using the data of the following table:

Line color	Known wavelength	Experimental spectrometer value
Violet	388.9 nm	4.5
Blue	468.6 nm	4.8
Green	501.6 nm	5.0
Yellow	587.6 nm	5.6
Orange	667.8 nm	5.8
Red	706.5 nm	6.5

• Now, we plot Experimental spectrometer value (y-axis) vs. known wavelength (x-axis)

Spectometer reading vs Known wavelength 7 6.5 6 5.5 y 0.0059x 2.0984 R2- 0.952 4.5 A 3.5 350 400 500 600 300 450 550 650 700 750 Known wavelength Spectometer reading LC

• This plot give the following equation of trendline:

y0.0059 +2.0984

where

y = spectroscope reading

x = wavelength

2) Step 2: calculate the corrected wavelength and percent error

• the data for the second table is:

Name of gas	Line color	Spectroscope reading	literature wavelength
Hydrogen	Red	6.0	656.2 nm
	Violet	5.8	410.1 nm
Helium	Red	6.5	706.5 nm
	Violet	4.5	388.9 nm
Neon	Red	6.0	633.3 nm
	Violet	4.4	433.0 nm

• Using the equation obtained from calibration curve, we can calculate the corrected wavelength for each spectroscope reading:

y0.0059 +2.0984

y-2.0984 0.0059

Name of gas	Line color	Spectroscope reading	Corrected wavelength
Hydrogen	Red	6.0	6.0 2.0984 661.29 nm 0.0059
	Violet	5.8	5.8 2.0984 627.39 nm 0.0059
Helium	Red	6.5	6.5 2.0984 746.03 nm 0.0059
	Violet	4.5	4.5 2.0984 407.05 nm 0.0059
Neon	Red	6.0	6.0 2.0984 661.29 nm 0.0059
	Violet	4.4	4.4 2.0984 -390.10 nm 0.0059

• Now we can calculate the percent error, with this equation:

Correct - Ref % error x 100% Ref

Name of gas	Line color	Corrected wavelength	Literature wavelength	% error
Hydrogen	Red	661.29nm	656.2 nm	661.29 656.2| 100%=0.78% 656.2
	Violet	627.39 nm	410.1 nm	$\frac{\left |627.39-410.1 \right | }{410.1}\times 100\, \%=\mathbf{52.98\, \%}$
Helium	Red	746.03 nm	706.5 nm	746.03 706.5 100%=5.60% 706,5
	Violet	407.05 nm	388.9 nm	$\frac{\left |407.05-388.9 \right | }{388.9}\times 100\, \%=\mathbf{4.67\, \%}$
Neon	Red	661.29 nm	633.3 nm	$\frac{\left |661.29-633.3 \right | }{633.3}\times 100\, \%=\mathbf{4.42\, \%}$
	Violet	390.10 nm	433.0 nm	390.10 433.0 100%9.91% 433.0