1. Suppose a diagnostic x-ray image (i.e. radiograph) for a patient requires 100 photons/mm² at the detector plane and the patient has 20 cm water equivalent thickness with only soft tissue in the beam path. If the radiograph was taken with a 20 KeV photon beam and a 100 keV photon beam, how much higher would the incident intensity, in photons/mm², need to be for the 20 KeV beam than with the 100 KeV beam? Use the following linear attenuation coefficients for μ. At 20 keV, μ = 0.76 cm^-1 and μ = 0.76 cm^-1 at 100 keV.

2. If another radiograph was taken for mammography with a 20 KeV beam penetrating thickness of 4 cm, what incident intensity would be required then? Assume that 100 photons/mm² is still required at the detector plane. How much higher or lower is this intensity compared to the 100 keV beam penetration 20 cm of soft tissue?