# Wavelength Uncertainty

1. Feb 3, 2012

### chill_factor

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

An excited atomic state has a lifetime of 1 ms.

What is the uncertainty in its energy?

The photon emitted during its decay is 550 nm in wavelength. What is the uncertainty and fractional uncertainty in its wavelength?

2. Relevant equations

ΔEΔt≥hbar/2

3. The attempt at a solution

a. Straightforward plugging into the equation.

ΔE = hbar/(2Δt) = 5.25x10^-32

b. Use ΔE=hΔf to find the frequency.

Δf = 79.6 s^-1

if I were to plug this into ΔλΔf=c, it results in a very large Δλ which is unphysical.

Δλ = ?????

2. Feb 3, 2012

### ardie

that is the right method. the result is not a wavelength, but an uncertainty in the wavelength, and it should be a fraction of 500nm

3. Feb 3, 2012

### chill_factor

The resulting uncertainty is in the hundreds of meters though =(

4. Feb 3, 2012

### vela

Staff Emeritus
While it's true that $\lambda f = c$, it doesn't follow that $\Delta \lambda \Delta f=c$.

5. Feb 3, 2012

### ardie

work out the energy associated with the transition, then work out the ratio of the uncertainty of the energy and the energy of the transition. the energy is related to the wavelength of a particle through the dispersion relation. assume a non relativistic electron's dispersion relation, and work out the wavelength uncertainty from there.