Question

After observing light from a fluorescent bulb as a series of colored bands through a spectroscope, a table is compiled with two columns. The left column corresponds to the independent variable -- the literature wavelength of each colored band and the right column is the dependent variable -- the position on the scale of the spectroscope at which each colored band appears. The data is plotted as a scatter plot and fitted to a line with the following equation: y= 0.0084x - 1.237. What is the wavelength that corresponds to a line which appears at 6.57 on the scale of a spectroscope?

a) 744.05 nm
b) 800.00 nm
c) 671.43 nm
d) 632.63 nm

Answer 1

To find the wavelength at a spectroscope scale reading of 6.57, we use the given equation y = 0.0084x - 1.237 to solve for x. However, the calculated value of 932.86 nm does not match any of the provided options, suggesting a potential mistake in the scatter plot data or the linear equation.

Step-by-step explanation:

The student is working with a spectroscope and has plotted data related to the emission spectra of a fluorescent bulb. The scatter plot of wavelength versus scale position is described by the linear equation y = 0.0084x - 1.237, where x represents the literature wavelength and y represents the corresponding position on the spectroscope scale.

To find the wavelength corresponding to a position of 6.57 on the scale, we simply plug the value into the equation and solve for x:

y = 0.0084x - 1.237
6.57 = 0.0084x - 1.237
x = (6.57 + 1.237) / 0.0084
x = 932.86 nm

However, this value is not among the answer choices provided. There appears to be a mistake since none of the answer options (a 744.05 nm, b 800.00 nm, c 671.43 nm, d 632.63 nm) match the calculated wavelength. The student should review the scatter plot data and equation for any potential errors.