Final answer:
To calculate the number of x-ray photons per second produced by an x-ray tube with 1.00 W power, convert the energy per photon from keV to joules, and divide the power by the energy per photon. The closest to the calculated value of 8.324 × 10¹⁶ photons/s is option b) 1.92 × 10¹⁶ photons/s.
Step-by-step explanation:
To find out how many x-ray photons per second are created by an x-ray tube that produces an x-ray flux with a power of 1.00 W, given that the average energy per photon is 75.0 keV, we first need to convert the energy from keV to joules since power is given in watts (joules per second).
1 eV = 1.602 × 10⁻¹¹ J, so 75.0 keV = 75,000 eV = 75,000 × 1.602 × 10⁻¹¹ J = 1.2015 × 10⁻¹⁵ J.
Next, we use the formula:
Number of photons per second = Power / Energy per photon
Number of photons per second = 1.00 W / (1.2015 × 10⁻¹⁵ J/ photon)
Number of photons per second = (1.00 J/s) / (1.2015 × 10⁻¹⁵ J/ photon) = 8.324 × 10¹⁶ photons/s.
Looking at the provided options, the closest value is option b) (1.92 × 10¹⁶) photons/s.