An electron (mass m , charge -e ) is moving with an initial velocity v = v₀ i ( v₀ > 0 ) in a region where a uniform electric field E = E₀ i ( E₀ > 0 ) is present. If the initial de-Broglie wavelength of the electron is ₀ , the distance travelled by the electron by the time its de-Broglie wavelength becomes n ₀ ( n > 1 ) is:

Step-by-step solution

Initial de-Broglie wavelength is ₀ = h mv₀ . When the de-Broglie wavelength becomes n ₀ , the new velocity v_f is given by: _f = h mv_f = n ₀ = n ( h mv₀ ) v_f = v₀ n The electric field is along the positive x-axis, so the force on the electron is along the negative x-axis. The acceleration is a = - eE₀ m . Using the third equation of motion, v_f^2 = u^2 + 2ax : ( v₀ n )^2 = v₀^2 - 2 ( eE₀ m )x 2 ( eE₀ m )x = v₀^2 - v₀^2 n^2 = v₀^2 (1 - 1 n^2 ) x = mv₀^2 2eE₀ (1 - 1 n^2 ) Answer: mv₀^2 2eE₀ (1 - 1 n^2 )