Final answer:
The kinetic energy of the electron with a de Broglie wavelength the same as that of a 100-keV x-ray is approximately 0.660 eV.
Step-by-step explanation:
The kinetic energy of an electron can be calculated using the equation:
KE = (1/2)mv^2
Where KE is the kinetic energy, m is the mass of the electron, and v is the velocity of the electron.
Given that the de Broglie wavelength of the electron is the same as that of a 100-keV x-ray, we can use the equation:
λ = h / mv
Where λ is the wavelength, h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron.
Since the wavelength is the same, we can equate the two equations:
(1/2)mv^2 = h / mv
Simplifying this equation, we get:
v = √(2h / m)
Substituting the given values, we have:
v = √(2 * 6.62607015e-34 J s / (9.11e-31 kg))
v = √(1.452227375) * 10^4 m/s
v = 120.5 km/s
Since the electron is nonrelativistic, we can use the classical kinetic energy equation to find the kinetic energy:
KE = (1/2)mv^2
Substituting the given values, we have:
KE = (1/2) * 9.11e-31 kg * (120.5 km/s)^2
KE = 0.6603 eV
Therefore, the kinetic energy of the electron is approximately 0.660 eV.