Originally posted by elfmotat
So, long time no see to anyone who remembers me. I had another thread like this, but it's well over 60 days old now so I'm not allowed to bump it.
If you want to know anything about, relativity, quantum mechanics, etc., you can ask me here.
I am a little bit stuck on part b of the following problem.
An unusually long-lived unstable atomic state has a lifetime of 1 ms. (a) Roughly what is the minimum uncertainty in its energy? (b) Assuming that the photon emitted when this state decays is visible (lambda =550nm), what are the uncertainty and fractional uncertainty in its wavelength?
For part (a) I solved and got delta E>= hbar/(2*delta_t) -> E=3.29*10^-13 ev
For part (b) I am a little bit unsure of how to go about getting delta_lambda, I tried multiple times but it seems like I end up with another unknown in my equations.
I found an answer key and it says the answers are (a)3.3*10^-13 ev (b) 8*10^-11 nm, 1.5*10^-13
I understand how the 1.5*10^-13 is obtained it is 8*10^-11/550 (assuming the 8 is rounded up and that the actual value is used in the calculation of the fractional uncertainty)
Could you show me how to derive delta_lambda from the uncertainty relations equations? I think it is the delta_t*delta_w >= 1/2 equation and then you can plug in delta_w=2*pi*delta_f but then how do you go from delta_f to delta_lambda, since you can't simply use lambda=c/f.
Thanks!