Kinetic energy of a proton is equal to energy E of a photon. Let ' λ₁ ' be the de-Broglie wavelength of proton and ' λ₂ ' be the wavelength of photon. If ((λ₁)/(λ₂)) ∝ Eⁿ then the value of ' n ' is (a) 1 (b) 2 (c) 5 (d) 0.5

Answer: (d). Proton: λ₁ = (h)/(√(2mE)). Photon: λ₂ = hc/E. (λ₁)/(λ₂) = (√(E))/(c√(2m)) ∝ E1/2 So n = 0.5: the answer is (d).

Kinetic energy of a proton is equal to energy E of a photon. Let ' λ₁… | MHT CET 2024 (16 May, Shift 2)

Q58MHT CET 2024 · 16 MAY · SHIFT 2Medium

Matter Waves: de Broglie Wavelength

Kinetic energy of a proton is equal to energy $E$ of a photon. Let ' $\lambda_1$ ' be the de-Broglie wavelength of proton and ' $\lambda_2$ ' be the wavelength of photon. If $\left(\frac{\lambda_1}{\lambda_2}\right) \propto E^n$ then the value of ' $n$ ' is

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Answer: (d)

Proton: $\lambda_1 = \dfrac{h}{\sqrt{2mE}}$ . Photon: $\lambda_2 = \dfrac{hc}{E}$ .
$\dfrac{\lambda_1}{\lambda_2} = \dfrac{\sqrt{E}}{c\sqrt{2m}} \propto E^{1/2}$
So $n = 0.5$ : the answer is (d).

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