Rydberg Formula, 1.13 HW

[Jacy Black 1C]

Okay so the Rydberg Formula in the book is stated as

V= R{(1/(n1)^2)-(1/(n2)^2}

This makes sense to me, but in the example of practice problem 1.13, I had trouble understanding which N given would be N1 and which would be N2.

1.13 asks to calculate the wavelength of radiation generated by the transition from N=4 4o N=2.

I assumed that N=4 would be N1, because it is the initial condition. Therefore, N2 would be the N=2. However, the answer in the solutions manual has it the opposite way, with N=2 as N1 and N=4 as N2.

Could someone please help explain this? Many thanks.

[Danielle Sumilang - 1F]

Hello!

In order to find the change in energy level, the equation is E(final)-E(initial). Another way of thinking about this is if the temperature is 40 degrees F in the afternoon but it drops to 20 degrees F in the night, the change in temperature is -20 degrees F (change in temperature= final temp - initial temp). So in the example you gave, the initial energy level is N=4 and the final energy level is N=2. Therefore N1 is N=2 and N2 is N=4.

[Joanna Pham - 2D]

So for these types of questions, should we always assume that N1 stands for the final energy level and N2 is the initial energy level?

[AnnaYan_1l]

Yes, I believe this would be the best way to look at it.

[Chem_Mod]

The Rydberg formula always looks for a positive number (frequency). So, n2 > n1 always.

If you want to look in terms of energy, then you must always do E(final) - E(initial). But then when you carry this out, you are probably thinking about the energy of the electron. So, when energy is lost (negative value), this means that you had a positive value of energy being emitted due to conservation of energy. So, this positive value = h*freq, and you can solve for frequency.