The maximum permissible workday dose for occupational exposure to radiation is 11 mrem.A 77-kg laboratory technician absorbs 2.3 mJ of 0.5-MeV gamma rays in a work day.The relative biological effectiveness (RBE)for gamma rays is 1.00.What is the number of gamma-ray photons absorbed by the technician in a workday?

Question

Quizplus · Accepted Answer

The energy of a single gamma-ray photon is:$$E = hf = \frac{hc}{\lambda}$$where h is Planck's constant, f is the frequency, c is the speed of light, and λ is the wavelength.The wavelength of a 0.5-MeV gamma ray is:$$\lambda = \frac{hc}{E} = \frac{(6.626 imes 10^{-34} ext{ J s})(3 imes 10^8 ext{ m/s})}{0.5 imes 10^6 ext{ eV}} = 2.49 imes 10^{-12} ext{ m}$$The number of gamma-ray photons absorbed by the technician is:$$N = \frac{E}{E_\gamma} = \frac{2.3 imes 10^{-3} ext{ J}}{2.49 imes 10^{-12} ext{ J}} = 9.24 imes 10^8$$Therefore, the number of gamma-ray photons absorbed by the technician in a workday is 3 × 10⁸.

The Maximum Permissible Workday Dose for Occupational Exposure to Radiation