Ratio of de Broglie wavelengths!

Classical Mechanics Level 2

Two particles of mass m m and 4 m 4m have equal kinetic energies. Find the ratio of their de Broglie \text{de Broglie} wavelengths.


The answer is 2.

Swapnil Das by Swapnil Das , 20, India

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1 solution

Rishabh Jain
Jan 22, 2016

λ = h p = h 2 K m ∝ 1 m \lambda=\dfrac{h}{p}=\dfrac{h}{\sqrt{2Km}}∝\color{forestgreen}{\dfrac{1}{\sqrt m}} Hence, λ 1 λ 2 = m 2 m 1 \dfrac{\lambda_1}{\lambda_2}=\sqrt{\dfrac{m_2}{m_1}} = 4 m m = 2 =\sqrt{\dfrac{4m}{m}}\Large =2 (where symbols have their usual meanings) \small{\color{#3D99F6}{\text{(where symbols have their usual meanings)}}}

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Nice and fast ;)

Swapnil Das - 5 years, 4 months ago

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