The graph which shows the variation of ((1)/(λ²)) and its kinetic energy, E is (where λ is de Broglie wavelength of a free particle): (a) (b) (c) (d)

Answer: (d). λ = (h)/(√(2mE)) ⇒ (1)/(λ²) = 2m/h²E. So (1)/(λ²) ∝ E: a straight line through the origin. So the answer is (d).

The graph which shows the variation of ((1)/(λ²)) and its kinetic… | NEET 2024

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Matter Waves: de Broglie Wavelength

The graph which shows the variation of $\left(\frac{1}{\lambda^2}\right)$ and its kinetic energy, $E$ is (where $\lambda$ is de Broglie wavelength of a free particle):

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Answer: (d)

$\lambda = \dfrac{h}{\sqrt{2mE}} \Rightarrow \dfrac{1}{\lambda^2} = \dfrac{2m}{h^2}E$ .
So $\dfrac{1}{\lambda^2} \propto E$ : a straight line through the origin.
So the answer is (d).

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