Phys 312 - Assignment 12

PLEDGED

Due Friday, May 1, 1998.

1.

Light of the day.

(a)

What is the intensity of solar radiation at noon today if the sky is clear, in W/m²? How many photons per second are arriving on a m²?

(b)

If you pass the direct sunlight through a polarizer, what fraction of the intensity goes through, at most?

(c)

How much current could the light generate at 120 V if all the power incident on 1 m² could be converted to electric power? How much can it generate in practice? Can a larger current be generated at 5 V? can more power be generated?

2.

Expansion of the universe

(a)

Does the expansion of the universe imply that the earth is getting bigger? The solar system? Our galaxy? The distance from our galaxy to the Virgo cluster?

(b)

If Hubble's constant is 70 Km/sec/Mpc, how far are galaxies that are moving away from us at one third of the speed of light? At even greater distances, the galaxies eventually move away from us at a speed exceeding the speed of light, if Hubble's law is valid. Is this possible?

(c)

If Hubble's constant is 70 Km/sec/Mpc, how old is the universe in the simplest model in which the ``radius'' increases in proportion to t^2/3? Justify your answer.

3.

Particle decays.

(a)

Name the particles involved in the process $n\rightarrow p+e+\bar{\nu}_{e}.$ Which are hadrons, mesons, baryons, leptons? Complete the following table

$$\begin{array} {lllll} & n & p & e & \bar{\nu}_{e} \\ & &... ...ber} & & & & \\ {\rm Electron\;number} & & & & \end{array}$$

(b)

Some of the particles in this process are made out of quarks. Describe the process in terms of the transformation of the constituent quarks.

(c)

Why are these decays forbidden?

i.

$n\rightarrow \ \pi ^{+}+e^{-}+\bar{\nu}_{e}$

ii.

$n\rightarrow e^{+}+e^{-}$

iii.

$n\rightarrow p+\mu ^{-}+\bar{\nu}_{\mu }$

iv.

$n\rightarrow \bar{p}+e^{+}+\nu _{e}$

4.

Smoke detectors. Read about them in Bloomfield. The one we looked at in class uses an ²⁴¹Am source with an activity of 1 $\mu$Ci = 37kBq.

(a)

Find out something more about ²⁴¹Am. How is it manufactured? Is it cheap and plentiful? How does it decay, mostly?

(b)

How many decays per second is 1 $\mu$Ci? How much ²⁴¹Am, in grams, gives out 1 $\mu$Ci?

How does ²⁴¹Am decay, mostly? After one year, how much is the activity of the decay product(s), compared to that of the remaining americium? (Is it significant?) Why is it important that the isotope used in a smoke detector not decay into a radioactive gas such as radon?

(c)

If you kept 1 $\mu$Ci of ²⁴¹Am in your mouth for an hour, would you get a bad dose of radiation? You can find out in Melissinos what is the permissible quantity of an ingested isotope, but here we have to worry about a local burn, rather than a whole-body effect.