Question

Question #d0cfc

Answer 1

Here's how you could do it:

Explanation:

It seems you need to produce a calibration curve for the distance measured against the wavelength of the emission line using Excel.

I got this from your data:

I assumed cm but I guess it could be mm - you should put this on your table.

Point 28 is an outlier - you should repeat this if you can.

I then used the 3 lines from the hydrogen lamp to read off the values of the wavelength.

I can't read your worksheet too well, it seems you are asked for a linear plot.

To do this enter your data in a table and make a scatter chart. Click on a data point and "add trend line". You can select "linear" and it will give you the line of best fit through the points.

You can select "display `"R"^2` value" as asked and also "display equation" which returns the equation of the straight line.

The `"R"^2` value is the square of the correlation coefficient for which I got `0.8747`.

This means the correlation coefficient `=sqrt(0.8747)=0.935` which is very close to an exact correlation of `1` - though I chose a binomial trend line.

I have manually read the wavelengths off the chart, though you could use the equation given.

So for red:

`d=33.1"cm"` and `lambda=659.4"nm"`

This is an experimental value. You are asked to compare this with the calculated value using the Rydberg Equation:

`1/lambda=R[1/n_1^2-1/n_2^2]`

`R=1.0974xx10^(7)" ""m"^(-1)`

The Balmer Series, which you are dealing with, involves transitions down to the `n=2` energy level:

The red emission line will be the lowest in energy so will have the longest wavelength corresponding to `n=3rarr2` .

Putting this into the Rydberg Expression:

`1/lambda=1.0974xx10^(7)[1/2^2-1/3^2]`

(You made a mistake in your annotation and wrote `1/2` instead of `1/2^2` )

`:.1/lambda=0.1524xx10^(7)" ""m"^(-1)`

`:.lambda=656.1" ""nm"`

So we have:

Experimental: `659.4" ""nm"`

Theoretical: `656.1" ""nm"`

That's reasonably good. You can work out the difference as a percentage as asked for in your error calculation.

Then work out `4rarr2` and `5rarr2` in the same way.