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## Homework Statement

Atoms of a certain material are in an excited state 1.8eV above the ground state and remains in that excited state for 2.0ms before to the ground state. Find

1) The frequency of the emitted photon

2) The wavelength of the emitted photon

3)The uncertainty in the energy of the emitted photon

4) The relative width of the special line [itex]\frac{ \Delta \lambda }{ \lambda }[/itex] and [itex]\frac{ \Delta f }{ f }[/itex] produced by these atoms.

I'm not really sure what 2.0 ms means, is that 2 milliseconds?

## Homework Equations

Well, I'm not entirely sure, this what I mostly need help with but I'll try my best in finding what equations I think should be used.

1.[itex]f = \frac{ E }{ h }[/itex]

2.[itex]\lambda=\frac{ c }{ f }[/itex]

3. [itex]\Delta t \Delta E \ge \frac{ h}{ 2 }[/itex]

4.[itex]\Delta \lambda = \lambda \frac{ \Delta E }{ E }[/itex] not exactly sure for this one.

## The Attempt at a Solution

Ok so using equation 1. [itex]f = \frac{ E }{ h }[/itex] = [itex]\frac{ 2.88*10^{-19}J }{ 6.626*10^{-34} Js } = 4.35*10^14 Hz[/itex]

2. [itex]\lambda=\frac{ c }{ f }[/itex] = [itex]\frac{ 3*10^8m/s }{ 4.35*10^14 Hz } = 6.9*10^-7m[/itex]

3. [itex]\Delta t \Delta E \ge \frac{ h}{ 2 }[/itex] = [itex]\Delta E = \frac{ h }{ \Delta t 2 } = \frac{ 6.626*10^{-34}Js }{ 0.002s(2) } = 2.66 *10^-31 J[/itex]

4. I'm not sure if my formula I gave for this one is correct, but I'll try it anyways and not sure for frequency?

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