Error equation for the balmer series

[wahaj]

Homework Statement

I have to find the error in λ determined by the Bohr model/Balmer series. I am a bit confused with this so I'd like someone to double check my work. I don't know the exact name of this method but basically all you do is take the differential of all the values which have an error to find the error of the determined value.

Homework Equations

$$\frac{1}{\lambda} = R (\frac{1}{n^2_f} - \frac{1}{n^2_i} )$$
n_f and n_i are discreet values so they have no error in them
R is the Rydberg constant and has an error of +-1 in the last digit so
R = (1.097 +- 1 ) * 10⁷ m^-1

The Attempt at a Solution

$$\frac{1}{\lambda} = R (\frac{1}{n^2_f} - \frac{1}{n^2_i} )$$
$$\frac{\delta \lambda}{\lambda^2} = \delta R (\frac{1}{n^2_f} - \frac{1}{n^2_i} )$$
$$\delta \lambda = \lambda^2 (\frac{1}{n^2_f} - \frac{1}{n^2_i} ) \delta R$$
The reason I am confused with this is that I am trying to find the error in λ but λ shows up on the right hand side of my error equation. Also did I get the error in R in the right decimal place?

 

[Simon Bridge]

First: replace everything in brackets with 1/K and solve for lambda.
Now find the error on lambda - should clear up your confusion.

 

[wahaj]

that works thanks

 

[dab353]

So is the equation supposed to look like as follows: δλ=λ2(1/K)δR? I am so confused.

 

[Simon Bridge]

@dab353: welcome to PF;
Take it step-by-step.
Start with the full equation.
Substitute the 1/K in for the brackets... that's just to make it clear.
Solve that equation for lambda.
Do the error analysis like normal.