Estimate the lifetime of the excited state that produced this line.

[stacker]

Homework Statement

An atomic spectrum contains a line with a wavelength centered at 460 nm. Careful measurements show the line is really spread out between 459 and 461 nm.

Estimate the lifetime of the excited state that produced this line.

Homework Equations

Change in Frequency = Speed of light/Change in Wavelength

Time = The inverse of frequency

The Attempt at a Solution

Change in wavelength = 461nm -459 nm = 2 nm or 2x10^-9 meters

Change in frequency = speed of light/change in wavelength = (3x10^8)/(2x10^-9) = 1.5x10^17 in units of s^-1

Life time = 1/(1.5x10^17) = 6.7*10^-18 seconds

But this is wrong and I don't know where to go from here. Please help!

 

[vela]

Neither of your relevant equations is correct. For the first one, use $\lambda_1 = c/f_1$ and use $\lambda_2 = c/f_2$ and find what $\lambda_1 - \lambda_2$ equals. The second equation only applies if the time is the period of oscillation, which it isn't in this case.

 

[fluidistic]

I'd have had approached the problem differently but I might be totally wrong.
Let me write the following to vela (please do not read this OP!):

Spoiler

Hey vela :)
I'd have used HUP for that one. So instead of looking for the delta lambda, I'd have looked for delta E and then apply the HUP to get delta t.
What do you think about the approach?

 

[vela]

Yeah, that's correct.