An electron with an initial de Broglie wavelength ₀ enters a uniform electric field. The direction of the electric field is perpendicular to the initial velocity of the electron. At a certain instant, the velocity vector of the electron makes an angle with its initial direction. The de Broglie wavelength of the electron at this instant is:

Step-by-step solution

Let the initial velocity of the electron be v₀ . The initial de Broglie wavelength is ₀ = h mv₀ . The electric field is perpendicular to the initial velocity, so it only accelerates the electron in the transverse direction. The component of velocity parallel to the initial direction remains constant. At the instant the velocity vector makes an angle with the initial direction, let the total speed be v . The component of velocity along the initial direction is v . Since this component is constant, we have: v = v₀ v