# Homework Help: Estimate the lifetime of the excited state that produced this line.

1. May 15, 2012

### stacker

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Change in Frequency = Speed of light/Change in Wavelength

Time = The inverse of frequency

3. 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

2. May 15, 2012

### vela

Staff Emeritus
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.

Last edited: May 15, 2012
3. May 15, 2012

### 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!):
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?

4. May 15, 2012

### vela

Staff Emeritus
Yeah, that's correct.