Gamma Rays

The highest frequency $(> 5 \time 10^{19} \, {\rm Hz})$ electromagnetic radiation is referred to as Gamma Rays. These are produced in nuclear transitions when the nucleus goes from an excited state to a lower energy state. These are produced in copious amounts in nuclear reactors and in nuclear explosions. Electron positron annihilation also produces Gamma rays. Typical energy range for Gamma radiation is in MeVs (million electron-volts). They penetrate through almost any material. One needs thick lead walls to stop Gamma rays. Gamma rays will ionize most gases, and is not very difficult to detect this radiation through this. Exposure to gamma rays can mutate and even kill living cells, and is very harmful for humans. Controlled exposure is used to kill cancerous cells and this is used for cancer treatment.

There are mysterious astrophysical sources which emit a very intense burst of Gamma rays. The exact nature of these sources is still a subject of intense study, and one of the theories is that these are hypernovae in distant galaxies.

Problems

1. Show that in the limit $h \nu/(k T) \ll 1$ the spectral energy density $u_{\nu}$ of blackbody radiation is proportional to $T$ ie. $U_{\nu} \propto T$. What is the constant of proportionality?
2. Use the Wien's displacement law to estimate the wavelength and corresponding frequency at which the radiation from the earth peaks. Assume it to be a blackbody at $T=300 \, {\rm K}$. Repeat the same for the sun assuming $T=6,000 \, {\rm K}$. For what value of $T$ does the peak shift to UV?
3. What is the wavelength range corresponding to X-ray?
4. Evaluate approximately the energy of a Sodium yellow photon ($\lambda$=589.3 nm).