To image a virus of linear size d , through what voltage electrons (mass ' | TestHub

Passage / Comprehension

Both the de Broglie hypothesis and Heisenberg's uncertainty principle establish that microscopic particles have a more prominent wave nature.

Heisenberg realized that, in the world of very small particles, one cannot measure any property of a particle without interacting with it in some way. This introduces an unavoidable uncertainty into the result. One can never measure all properties exactly. The minimum uncertainty in the position of any body is given by the wavelength of light. Heisenberg’s uncertainty principle states: $Δ x Δ P \geq \frac{h}{4 π} = \frac{ℏ}{2}$

To image a virus of linear size d , through what voltage electrons (mass ' m ' and charge ' e ') should be accelerated in electron microscope.

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Solution:

To image a linear size $d$ , we need $λ \leq d$ .

$∵ λ = \frac{h}{p} ∴ d ⩾ \frac{h}{p} = \frac{h}{2 m e V} ∴ V ⩾ \frac{h ^{2}}{2 m e d ^{2}} ∵ h = \frac{h}{2 π} ∴ V ⩾ \frac{h ^{2} 2 π ^{2}}{m e d ^{2}}$

Chemistry - Atomic Structure Question with Solution | TestHub

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