I need to derive an error equation for Bohr's model to use in my physics lab this week. I am really bad at calculus, so if anyone can help me that would be really great.

the equation is

(1/lambda)=R[(1/n^2final)-(1/n^2initial)]

I've never had to derive anything like this before. Even if someone could tell me HOW to do it, I'll be happy to do it myself.

Thanks

error in what? I am uncertain of what your goal is.

Hi Bob, I have to derive the error in the wavelength. I only know how to derive error equations from multiplication or addition/subtraction.

For example, if I needed to derive an arror equation for N=MT it would be deltaN=(deltaM+deltaT)N

So how do I do it for a division question?

sorry, edit, that would be (deltaM/M + deltaT/T)N

Sure! I can guide you through the process of deriving the error equation for Bohr's model equation.

To clarify, you are interested in finding the error or uncertainty in the wavelength (lambda) when measuring the energy levels of an electron transitioning from an initial energy level (n_initial) to a final energy level (n_final), given by the equation:

(1/lambda) = R * [(1/n^2_final) - (1/n^2_initial)]

Here's how you can proceed:

1. Start by differentiating the equation with respect to each variable involved, keeping in mind that lambda, n_initial, n_final, and R are the variables. Since you're interested in deriving the error equation, consider all variables as having uncertainties associated with them.

2. Apply the "chain rule" of differentiation to each term. The chain rule states that when you differentiate a function of a function, you multiply the derivative of the outer function by the derivative of the inner function.

3. For example, let's consider differentiating the equation with respect to lambda:
- The derivative of (1/lambda) is -1/lambda^2.
- Since lambda itself has an uncertainty associated with it, let's denote it as d(lambda).

4. Now, differentiate the equation with respect to n_initial and n_final. Assuming each of these has its own uncertainty (d(n_initial) and d(n_final)), apply the chain rule as mentioned above.

5. Finally, differentiate the equation with respect to R, assuming it has an uncertainty d(R). Again, apply the chain rule accordingly.

6. Now that you have derived the equation with all the different differentials, you can isolate the uncertainty terms (d(lambda), d(n_initial), d(n_final), d(R)) and solve for the uncertainty in lambda (d(lambda)).

Remember that all these uncertainties arise from the differentials, which signify small variations or errors in the respective variables. Therefore, when using the error equation, you can substitute the relevant uncertainties into it to calculate the overall uncertainty in lambda.

I hope this explanation helps! If you have any further questions or need additional clarification, feel free to ask.