physics GRE-astronomy/optical help-stat help

[lifes3ps]

really lost, dont know what to solve for.

2 stars are separated by an angle of 3*10^(-5). whats diameter of smallest telescope that can resolve the two stars using visible light (600nm)? ignore atmospheric interference

(2.5cm)

2. student makes 10 1second measurements of the disintegration of a sample of a long lived radioactive isotope and obtains the following values:
3,0,2,1,2,4,1,2,5

how long should person count to establish an uncertainty of 1 percent?

i hardly know what theyre asking for here. half life?

[evank15]

I have no idea what the second question is asking, but the first one is simple. Just have to know what formula to use.

The (angular) resolution limit is known as the Rayleigh Criterion.

This limit, x, is a function of the diameter of the telescope and the wavelength of light.

sin(x) = 1.22k/D

where k is the wavelength of light and D is the diameter of the telescope. Invoking the small angle approximation (extremely valid here), sin(x) ~ x, we get for the formula you want:

D = 1.22k/x

D = 1.22(600E-9)/(3E-5)

D = 2.44cm

[Max Raker]

What units are the measurements in problem 2?

[gumpzilla]

[ QUOTE ]

2. student makes 10 1second measurements of the disintegration of a sample of a long lived radioactive isotope and obtains the following values:
3,0,2,1,2,4,1,2,5

how long should person count to establish an uncertainty of 1 percent?

i hardly know what theyre asking for here. half life?

[/ QUOTE ]

So in 10 seconds, you have 20 counts. So assume the average rate is 2 counts per second. The physics aspect is that you're supposed to know that the uncertainty for this kind of random process goes like root N, where N is the number of counts. Put into relative terms, like the question asks for, the relative uncertainty should go like 1 over root N. That will be one percent when root N is 100, or N = 10000 counts. At 2 counts per second, that should take about 5000 seconds.