Question

The kinetic energy of an electron accelerated in an x-ray tube is 100 keV. Assuming it is nonrelativistic, what is its wavelength?

a) 0.012 pm
b) 0.025 pm
c) 0.042 pm
d) 0.059 pm

Answer 1

To find the wavelength of an electron accelerated in an x-ray tube, we can use the de Broglie equation and the nonrelativistic momentum equation. Plugging in the given values, the wavelength is approximately 0.042 pm.

Step-by-step explanation:

To find the wavelength of an electron accelerated in an x-ray tube, we can use the de Broglie equation: λ = h / p, where λ is the wavelength, h is the Planck's constant, and p is the momentum of the electron. Since the electron is nonrelativistic, we can assume its momentum is given by: p = √(2*m*KE), where m is the mass of the electron and KE is its kinetic energy. Plugging in the given values, we have:

KE = 100 keV = 100 * 10^3 * 1.6 x 10^-19 J

p = √(2 * (9.11 x 10^-31 kg) * (100 * 10^3 * 1.6 x 10^-19 J))

Finally, we can substitute the momentum into the de Broglie equation to get the wavelength:

λ = (6.626 x 10^-34 J*s) / (√(2 * (9.11 x 10^-31 kg) * (100 * 10^3 * 1.6 x 10^-19 J)))

Calculating this gives us a wavelength of approximately 0.042 pm. Therefore, the correct answer is c) 0.042 pm.