# Homework Help: Decay lifetime

1. May 1, 2006

### square_imp

My question relates to calculating the decay lifetime of an unstable isotope. The information given is the average energy of the emitted gamma ray from the decay has an average energy of say 100kev and a line-width of 5 x 10^-6ev. From this information I need to work out the average lifetime for the isotope.

From what I can gather the problem seems to be similar to the Doppler shift effect. From the equation E = hf the energy of the gamma ray is related to its frequency and therefore the change in frequency can be worked out. Does the line width mean the upper and lower boundry of the gamma ray energy with the 100keV in the middle of that range? The other thing is that the shift of the energy either means the source is moving or the energy of the gamma rays emitted is changing for some other reason. The relation between this and the lifetime is not obvious to me. Any help would be much appreciated. I am probably missing something obvious.

2. May 1, 2006

### nrqed

To *me*, this seems to be an application of the time-energy Heisenberg uncertainty principle. Have you covered that?

3. May 1, 2006

### square_imp

From what I recall we have covered parts of the Heisenberg uncertainty principle, to note the position-momentum relationship. I will have a look and see what I can find about the time-energy relationship. I presume it will be similar to the position-momentum relationship.

4. May 1, 2006

### square_imp

From looking at the Heisenberg Principle again I find the relation as follows:

Energy uncertainty x Time uncertainty = Planks constant / 4 x pi

This is an equation describing that both the time and energy of a particle cannot be simultaneously accurately measured. The connection with my original problem I still cannot see really.

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