CBSE Class 12 · 2016 · Delhi · Modern PhysicsShort Answer

Plot a graph showing the variation of de-Broglie wavelength

λ

versus

\frac{1}{V}

, where

V

is the accelerating potential, for two particles A and B carrying the same charge but of masses

m_{1}

and

m_{2}

(m_{1} > m_{2})

. Which one of the two represents a particle of smaller mass and why?

Answer: The steeper line is the smaller mass $m_{2}$ (slope $\propto 1/ m$ ).

Solution

λ = \frac{h}{2 m q V} = (\frac{h}{2 m q}) \frac{1}{V},

so a graph of

λ

against

\frac{1}{V}

is a straight line through the origin with slope

\frac{h}{2 m q} \propto \frac{1}{m}

.
A smaller mass gives a larger slope (steeper line). Hence the steeper line (line 2) represents the particle of smaller mass

m_{2}

Steeper line \Rightarrow smaller mass (m_{2})

CBSE Class 12 Board · 2016 · Delhi · Subjective