Dual Nature of Matter

JEE Main level, single correct, medium

34 of 200

Question 34 of 200

Electron beam used in an electron microscope, when accelerated by a voltage of 20kV20kV has a de-Broglie wavelength of λ0{\lambda }_{0}. If the voltage is increased to 40kV40kV then the de-Broglie wavelength associated with the electron beam would be:

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Answer: (D) λ02\dfrac{{\lambda }_{0}}{\sqrt{2}}

The de-Broglie wavelength of an electron accelerated through potential VV is
λ=hmv=h2m(KE)=h2meV\lambda =\dfrac{h}{mv}=\dfrac{h}{\sqrt{2m(KE)}}=\dfrac{h}{\sqrt{2meV}}
where, hh is Planck's constant, ee is charge of electron and mm is mass of electron.
From above relation, λ∝1V\lambda \propto \dfrac{1}{\sqrt{V}}
∴λλ0=2040∴\dfrac{\lambda }{{\lambda }_{0}}=\sqrt{\dfrac{20}{40}}
⇒λ=λ02\Rightarrow \lambda =\dfrac{{\lambda }_{0}}{\sqrt{2}}.

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