Two lines A and B shown in the graph represent the de Broglie wavelength (lambda) as a function of 1/root(V) - Physics - Dual Nature Of Radiation And Matter

Question

Two lines A and B shown in the graph represent the de Broglie
wavelength (lambda) as a function of 1/root(V) (V is the
accelerating potential) for two particles having the same charge
Which of the two represents the particle of smaller mass?

Ujjval Chauhan · Accepted Answer

Dear student

The deBroglie wavelength is given by λ=hp=h2mEif charge accelerated by potential V then energy E=qV soλ=h2mqVλ=h2mq1Vλ=β1Vwhere β=h2mq slope of the line
so for same charge higher slope corresponding to lower mass
Hence B has the smaller mass

Two lines A and B shown in the graph represent the de Broglie wavelength (lambda) as a function of 1/root(V) (V is the accelerating potential) for two particles having the same charge. Which of the two represents the particle of smaller mass?