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(C) The de Broglie wavelength $\lambda$ of an electron with kinetic energy $E$ is given by the formula: $\lambda = \frac{h}{\sqrt{2mE}}$.When the kine

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$2 \lambda$

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(C) The de Broglie wavelength $\lambda$ of an electron with kinetic energy $E$ is given by the formula: $\lambda = \frac{h}{\sqrt{2mE}}$.When the kinetic energy becomes $E' = \frac{E}{4}$,the new de Broglie wavelength $\lambda'$ is:$\lambda' = \frac{h}{\sqrt{2mE'}} = \frac{h}{\sqrt{2m(\frac{E}{4})}}$.Simplifying the expression:$\lambda' = \frac{h}{\sqrt{\frac{2mE}{4}}} = \frac{h}{\frac{1}{2}\sqrt{2mE}} = 2 \left( \frac{h}{\sqrt{2mE}} \right)$.Substituting $\lambda$ into the equation:$\lambda' = 2\lambda$.

The de Broglie wavelength of an electron having kinetic energy $E$ is $\lambda$. If the kinetic energy of the electron becomes $\frac{E}{4}$,then its de Broglie wavelength will be:

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