Question

two lines A and B shown in graph plot the de broglie waves length as a function of 1/√V, ( V the accelerating potential ) for two particles having the same charge.which of the two represent the particles of larger mass? justify your answer .​

Answer 1

No graph has been supplied in the question. However, if given any graph, deduce as below.

Assumption: the graph has DBW on the y-axis, and 1/√V on the x-axis.

We know, that the de Broglie wavelength for a particle of charge q, accelerated from rest through a potential difference V, and of mass m, is given by:

$\lambda_{db} = \frac{h}{\sqrt{2mqV}}$

Therefore, the graph drawn between $\lambda_{db}$ and $\frac{1}{\sqrt{V}}$ must be a straight line, with slope proportional to $\frac{1}{\sqrt{m}}$ and $\frac{1}{\sqrt{q}}$.

Given that the two particles have the same charge, we only consider the proportionality of $\frac{1}{\sqrt{m}}$, and hence, the graph with higher slope shall correspond to the particle having lesser mass.