Question

An electron is moving will an initial velocity V = V₀i and is in a magnetic field B = B₀j. Then its deBroglie wavelength

(1) remains constant

(2) increases as the electron moves round a circular path

(3) decreases as the electron moves round a circular path

(4) increases and decreases periodically

Answer 1

(1) remains constant

When a particle moving in a direction perpendicular to the direction of the applied field the force acting on the electron is perpendicular to both the direction of moving particle and the field direction [F = -ce(V x B)]. Hence the magnitude of the velocity of the moving particle will not change and so its momentum remains constant. As λ = h/p, therefore λ will remain constant.