Solving for R in Atomic Spectroscopy | Get Homework Help and Tips

[mainzelmadchen]

Homework Statement

For our lab, we looked through the spectrometer to find the spectral values for Helium, which after being plugged into an excel spreadsheet, yielded an equation which I could use to find the wavelengths for Hydrogen. We were told to solve for R, which I did. However, at the end, all of my values have a 99.9% error! Even when I use my professor's wavelength values, I do not get the actual value of R = 1.10x10^-7 m-1. Am I calculating this wrong? My professor's wavelength values for #1,2,&3 respectively are 675, 450, & 415 nm.

Homework Equations

1/λ = R ((1/2^2)-(1/ninitial^2))

The Attempt at a Solution

1) 1/748.60606 nm = R ((1/2^2)-(1/3^2)); 0.0013358161 = R ((1/4)-(1/9)); 0.0013358161 = R (0.13888889); R = 0.0096178758 nm x (1 m/1 x 10^9 nm) = 9.6178758 x 10^-12 = 9.6 x 10^-12

2) 1/460.72727 nm = R ((1/2^2)-(1/4^2)); 0.0021704815 = R ((1/4)-(1/16)); 0.0021704815 = R (0.1875); R = 0.011575901 nm x (1 m/1 x 10^9 nm) = 1.1575901 x 10^-11 = 1.2 x 10^-11

3) 1/384.96970 nm= R ((1/2^2)-(1/6^2)); 0.0025976070 = R ((1/4)-(1/36)); 0.0025976070 = R (0.22222222); R = 0.011689232 nm x (1 m/1 x 10^9 nm) = 1.1689232 x 10^-11 = 1.2 x 10^-11

 

[mfb]

1/748.60606 nm
[...]
R = 0.0096178758 nm x (1 m/1 x 10^9 nm)

nm should be in the denominator in both cases. This would have been easy to spot if you did not drop the units in between.
It is the same for the other calculations.

 

[mainzelmadchen]

Ok, I see what you mean. At the end, I should have done (for number one) R = 0.0096178758 nm^-1 x (1 x 10^9 nm/1 m) which results in 9.6178759 x 10^6 m^-1. My answer is even more off. I tried this with my instructor's value to see if I get the correct answer. I did 1/675 nm = R ((1/2^2) - (1/3^2)) and got the result of 1.0666667 m^-1 x 10^7 and it should be 1.10x10^-7 m-1. Is there something else I am not doing correctly?

 

[mainzelmadchen]

I think I figured it out. I think my instructor made a mistake on this. I believe the answer should be 1.10 x 10^7 m^-1 and not 1.10 x 10^-7 m^-1. After calculating the normal equation constants, this is what I came up with.
1/wavelength = (2.18 x 10^-18 J / ((6.63 x 10^-34 J x s)(3.00 x 10^8 m/s)) x ((1/2^2)-(1/ninitial^2))

1/wavelength = (1.0960282 x 10^7 m^-1) x ((1/2^2)-(1/ninitial^2))

 

[mfb]

As a simple cross-check, R should have the same order of magnitude as 1/λ.
1.10 x 10^7 m^(-1) looks good, 1.10 x 10^(-1) m^(-1) is wrong.