High-purity germanium (HPGe) crystals are used as detectors for x rays and gamma rays. On interacting with the crystal, incoming photons produce electron-hole pairs, exciting many electrons across the 0.72 eV energy gap into the conduction band. The decay of the radioisotope Co results in the emission of two gamma rays with energies 1.17 MeV and 1.33 MeV (see Chapter 11).

(a) Compute the numbers of electrons N₁ and N₂ excited across the energy gap by each of the two gamma rays. 

(b) The numbers N₁ and N₂ are subject to statistical fluctuations of ±√N₁ and ±√N₂. Compute the fractional uncertainties in N₁ and N₂.

(c) Compute the corresponding fractional uncertainties in the energies of the two gamma rays. This is a measure of the energy resolution of the HPGe crystal.