Question

An xray tube has an applied voltage of 100 kV.

(a) What is the most energetic xray photon it can produce? Express your answer in electron volts and joules.
a) (1.602 times 10¹⁴) eV, (2.565 times 10¹⁶) J
b) (1.602 times 10¹⁵) eV, (2.565 times 10¹⁷) J
c) (1.602 times 10¹³) eV, (2.565 times 10¹⁵) J
d) (1.602 times 10¹⁶) eV, (2.565 times 10¹⁸) J

Answer 1

The most energetic x-ray photon produced by a 100 kV x-ray tube is 100 keV or 1.602 x 10⁻¹⁴ J, with its wavelength being approximately 0.124 nm.

Step-by-step explanation:

The most energetic x-ray photon an x-ray tube with an applied voltage of 100 kV can produce is 100 keV, which is the same as the applied voltage. This energy in electron volts is 100,000 eV since 1 keV = 1,000 eV. The energy in joules can be calculated using the conversion factor where 1 eV = 1.602 x 10⁻¹⁹ J. Therefore, the energy in joules is 100,000 eV x 1.602 x 10⁻¹⁹ J/eV = 1.602 x 10⁻¹⁴ J.

To find the wavelength of the most energetic x-ray, we use the equation E = hc/λ, where E is energy, h is Planck's constant (6.626 x 10⁻³⁴ m² kg/s), and c is the light's speed (3.00 x 10⁸ m/s). Rearranging the equation for wavelength (λ) gives λ = hc/E.

Plugging in the values, we get the wavelength λ = (6.626 x 10⁻³⁴ m² kg/s)(3.00 x 10⁸ m/s) / (1.602 x 10⁻¹⁴ J) which calculates to approximately 1.24 x 10⁻¹⁰ m or 0.124 nm.