# Using the data provided below, calculate the corrected wavelength for a spectroscope reading of 6.32.

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## Question:

Using the data provided below, calculate the corrected wavelength for a spectroscope reading of 6.32. Spectroscope Readings Known Helium Wavelengths (nm)
3.65 388.9
4.75 486.6
4.90 501.6
5.65 587.6
6.45 667.8
7.00 706.5

646.6 nm

Explanation:

Using the data given, we fit a linear model :

Spectroscope Readings Known Helium Wavelengths (nm)

3.65 388.9

4.75 486.6

4.90 501.6

5.65 587.6

6.45 667.8

7.00 706.5

Using technology like excel to fit the model, the regression model obtained is :

Y = 97.96582X + 27.48458

Where, y is the predicted or corrected wavelength value.

This mod could be used to calculate the corrected wavelength for a given Spectroscope value :

Given a Spectroscope value of 6.32 ; the corrected wavelength is obtained by replacing x in the equation by 6.32 and calculate y ;

x = 6.32

Y = 97.96582(6.32) + 27.48458

Y = 619.1439824 + 27.48458

Y = 646.6285624

Corrected wavelength value is : 646.6

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