# Physics307L:People/Mondragon/Notebook/071121

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## Contents |

## calibration

^{SJK 21:45, 1 December 2007 (CST)}using mercury to calibrate. center of slit, measuring clockwise

color | actual wavelength | measured wavelength |
---|---|---|

red | 690.75nm | 634nm |

yellow | 579nm | 545nm |

yellow | 577nm | 542nm |

green | 546.1nm | 525nm |

violet | 435.8nm | 422nm |

so the calibration curve is

## the hydrogen spectrum

^{SJK 21:49, 1 December 2007 (CST)}color | Measured Value | Actual Wavelength (nm) | Actual Wavelength (m) | 1/wavelength | n | 2^{ − 2} − n^{ − 2} | Rydberg Constant |
---|---|---|---|---|---|---|---|

red | 604 | 650.5060546 | 6.50506E-07 | 1537264.708 | 3 | 0.138888889 | 1.1068306E+07 |

blue green | 466.5 | 484.927823 | 4.84928E-07 | 2062162.558 | 4 | 0.1875 | 1.0998200E+07 |

violet | 421 | 430.1364809 | 4.30136E-07 | 2324843.496 | 5 | 0.21 | 1.1070683E+07 |

faint violet | 400.2 | 405.0890102 | 4.05089E-07 | 2468593.259 | 6 | 0.222222222 | 1.1108670E+07 |

mean value for Rydberg constant= standard deviation

## CALCULATIONS

heres the excel file Image:L and T Balmer series.xlsx Section above has numbers from the excel file.

here is a more careful analysis

Linefit says the calibration data fits the line

## Error propagation

No data on measurement error was ever taken, so, for any measurement of wavelength the error on the calculated actual value will be

The calculated Rydberg constant is related to the measured wavelength value thusly

Where λ_{m} is the wavelength measured by the instrument, *m* is the slope of the calibration curve, and *b* is the y intercept of the curve. Because of the uncertainty in the fit, the calculated value of the Rydberg constant will have uncertainty.

The uncertiainty in R_{H} is just R_{H} times the relative uncertainty in the calculated wavelength.

color | n | Accepted Wavelength (nm) | Measured Value | Calulated Actual Wavelength (nm) | Calculated Error(nm) | Relative Error | Actual Wavelength (m) | Rydberg Constant | Rydberg uncertainty |
---|---|---|---|---|---|---|---|---|---|

red | 3 | 656 | 604 | 650.506 | 48.684 | 0.074840 | 6.50506E-07 | 1.10683E+07 | 8.284E+05 |

blue green | 4 | 486 | 466.5 | 484.928 | 44.822 | 0.088305 | 4.84928E-07 | 1.09982E+07 | 9.712E+05 |

violet | 5 | 434 | 421 | 430.136 | 40.882 | 0.095044 | 4.30136E-07 | 1.10707E+07 | 1.0522E+06 |

faint violet | 6 | 410 | 400.2 | 405.089 | 39.994 | 0.098731 | 4.05089E-07 | 1.11087E+07 | 1.0968E+06 |

Average for Rydberg constant= . Uncertainty of average = . Accepted value =