Two isolated charged particles having masses m and 4m and charges +q and -2q respectively are initially held at rest at a certain distance apart. They are then released and allowed to move towards each other under their mutual electrostatic attraction. Assuming no other forces act on them, what will be the ratio of their de Broglie wavelengths at any instant before they collide?

Step-by-step solution

Since no external forces act on the two-particle system, the total linear momentum is conserved. Initially, both particles are at rest, so the initial momentum of the system is zero. At any instant during their motion, the sum of their momenta must be zero: p ₁ + p ₂ = 0 | p ₁| = | p ₂| = p The de Broglie wavelength is given by = h p . Since both particles have the same magnitude of momentum at any instant, their de Broglie wavelengths will be equal. Therefore, the ratio ₁ : ₂ = 1 : 1 . Answer: 1 : 1