If electron are accelerated from rest through a potential difference of 10kv, what is the wavelength of the associated electron [m = 9.1 x 10-31kg, e = 1.6 ...

If electron are accelerated from rest through a potential difference of 10kv, what is the wavelength of the associated electron

[m = 9.1 x 10-31kg, e = 1.6 x 10-19C, h = 6.6 x 10-34js]

Answer Details

The problem involves calculating the wavelength of an electron accelerated through a potential difference of 10kV, given the mass of the electron (9.1 x 10^-31 kg), the charge of the electron (1.6 x 10^-19 C), and Planck's constant (6.6 x 10^-34 Js). The formula for the wavelength of an electron is λ = h / (mv), where h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron. To find the velocity of the electron, we can use the formula for the kinetic energy of a particle, which is K = (1/2)mv^2 = eV, where K is the kinetic energy of the electron, e is the charge of the electron, and V is the potential difference through which the electron is accelerated. Solving for v, we get v = sqrt(2eV/m). Substituting the given values, we get v = 5.93 x 10^6 m/s. Finally, substituting the values of h, m, and v into the formula for the wavelength of the electron, we get λ = 1.22 x 10^-11 m, which is the first option. Therefore, the answer is: 1.22 x 10^-11 m.