General Astronomy, 29:61
Fall, 2005
Seventh Homework Set...October 14, 2005.
Due October 21, 2005

Show calculations and give reasons for your answers.

(1) The radioisotope Strontium 90 ($_{38}Sr^{90}$) has a half life of 28.8 years to a beta-decay reaction,

$$_{38}Sr^{90} \rightarrow _{39}Y^{90} + e + \nu$$ (1)

You obtain a sample which has 0.2 micrograms (1 microgram = $10^{-6}$ grams) of $_{38}Sr^{90}$. How many nuclei of $_{38}Sr^{90}$ are in the sample?

(2) Continue thinking about the decay of the Strontium 90 sample in the previous problem. What is the number of decays per second you would measure with a Geiger counter, or other apparatus? Hint: Here is a good opportunity to employ your differential calculus in a science problem.

(3) In class we discussed the exponential decay law for the number of radioisotopes as a function of time, and showed that at $t=T_{\frac{1}{2}}$ ( $T_{\frac{1}{2}}$ is the half life of the radioisotope) there are half as many radioactive nuclei as at $t=0$. Use this exponential decay law formula to prove that for any time $t> 0$, there are twice as many parent nuclei as there will be at $t+T_{\frac{1}{2}}$.

(4) A very fast coronal mass ejection can leave the Sun at a speed of 1000 km/sec. If it ``blasts off'' straight towards the Earth (this happens), how long after the CME eruption occurs will it arrive at Earth?

(5) Find a picture of the Sun which contains one or more sunspots. There are many places where you can find them. One easy possibility is the SOHO spacecraft web page which is on the course web page under ``SOHO views the Sun''. Look at ``images by date'', and note that you can choose earlier dates than those listed. Fish around until you find some good ones.

What is the diameter of the sunspot or sunspots you have chosen? If the sunspot is perfectly black, how much (i.e. by what percentage) would it reduce the solar constant?