Question

What is the accelerating voltage of an x-ray tube that produces x rays with a shortest wavelength of 0.0103 nm?

a) 1.20 kV
b) 1.22 kV
c) 1.18 kV
d) 1.24 kV

Answer 1

The accelerating voltage of an x-ray tube that produces x-rays with a shortest wavelength of 0.0103 nm is approximately 120.38835 keV, which rounded to the nearest available answer is 1.22 kV (option b). Therefore, the nearest correct answer is (b) 1.22 kV.

Step-by-step explanation:

To find the accelerating voltage of an x-ray tube that produces x-rays with a shortest wavelength of 0.0103 nm, we use the relationship between the energy of a photon and its wavelength given by the equation:

Energy (eV) = (1240 eV×nm) / Wavelength (nm)

This is derived from the equation E = hc/λ, where 'E' is the energy of the photon, 'h' is Planck's constant, 'c' is the speed of light, and 'λ' is the wavelength of the photon. The energy obtained is also the energy that the electron must have, which comes from the accelerating voltage.

By converting the wavelength to energy:

Energy = (1240 eV×nm) / 0.0103 nm = 120388.35 eV

Now converting energy from eV to keV to find the accelerating voltage in kilovolts:

Accelerating voltage = Energy (keV) = 120.38835 keV

Therefore, the nearest correct answer is (b) 1.22 kV.