Calculating the Excited State Lifetime of 223Ra Nucleus

[phyguy321]

Homework Statement

the nucleus of ²²⁷Th decays to ²²³Ra and $$\alpha$$. the daughter nucleus is left in a short lived excited state and decays down to the ground state with the emission of an 80 keV gamma ray. the natural line width of this gamma ray is .6 keV. what is the lifetime of the excited state of the ²²³Ra nucleus?

Homework Equations

$$\Delta$$E $$\Delta$$t = $$\hbar$$/2 where $$\Delta$$t is the lifetime $$\tau$$

The Attempt at a Solution

can i just solve for $$\Delta$$t as the lifetime of the excited state? letting $$\Delta$$E = 80 keV? I am not sure what to do with the line width, it's not in my book anywhere.

 

[quantumdude]

The 80 keV photon isn't the thing that determines the lifetime of the state. Check this out and see if it doesn't clear things up.

http://www.mwit.ac.th/~Physicslab/hbase/quantum/parlif.html

 

[phyguy321]

so the .6 keV is our uncertainty energy?
so $$\Delta$$t =hbar/2E