Plot a graph showing variation of de Broglie wavelength λ versus $fraction numerator 1 over denominator square root of straight V end fraction$ , where V is the is accelerating potential for two particles A and B, carrying the same charge but different masses m₁ and m₂ (m₁ > m₂). Which one of the two represents a particle of smaller mass and why?

Solution

Given,
Charge (q) is the same but the mass of both particles is different (m₁ > m₂).
The De-broglie wavelength given by,

$straight lambda space equals space fraction numerator straight h over denominator square root of 2 mqV end root end fraction$
The slope of the graph of λ versus $fraction numerator 1 over denominator square root of straight V end fraction$ = $fraction numerator straight h over denominator square root of 2 mqV end root end fraction$

The slope of the smaller mass is larger; therefore, plat A in the above graph represents mass m₂.

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