User:Jason O Archer/Notebook/PHYC 307L Junior Lab/2008/11/16

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Balmer Series Lab 11/16/08

Data Analysis

The exponential calibration curve we obtained from Excel is as follows:

λ' = 400 + 1.0667*(λ - 400)0.9853, where

  • λ' = actual wavelength
  • λ = measured wavelength

(This curve had an R2 value of 1 in Excel; the polynomial curves had lower values, so we used the exponential curve. We also chose the exponential curve since the error seemed to grow very fast with the increase in value very sharply.)

Note: The shifts of 400 came from an attempt to get the best possible fit for the exponential curve by having a starting point close to the origin.

From this curve, we can calculate the wavelengths measured for regular hydrogen and deuterium to be as follows:

Measured Wavelength for Hydrgen and Deuterium (nm) 410-411 434-435 486-487 659-660
Actual Wavelength for Hydrogen and Deuterium (nm) 410-411 434-435 486-487 655-656
Number n to which Wavelength Corresponds 6 5 4 3

From the equation λ-1 = R(2-2 - n-2), where

  • λ = spectral line wavelength,
  • R = Rydberg constant,
  • n = integer greater than 2

we can make calculations for the Rydberg constant. From calculation in Excel, we obtain the following eight values (in 1/m):

Wavelength Rydberg
410 10967264.32
411 10940192.81
434 10961127.61
435 10936012.3
486 10975701.82
487 10953513.54
655 10999003.1
656 10982753.03

The average value we calculate is 10964446.07 ± 7548.89 1/m. (mean ± SEM).

Since the official value is given as 10967758 1/m, we calculate the percent error to be an astonishingly low 0.0302%.

The Rydberg constant for hyrdogen is 10967758 1/m, as we are given. The Rydberg constant for deuterium, by the formula R = μe4/8ε02ch3, where

  • μ = reduced mass of the nucleus
  • e = elementary charge
  • ε0 = electrical constant
  • c = speed of light
  • h =- Planck's constant

we can calculate R to be 11055173 1/m for deuterium; this is a low 0.7970% difference.