How fast is an electron moving if it has a wavelength equal to the distance it travels in one second?

How fast is an electron moving if it has a wavelength equal to the distance it travels in one second?
  1. $\sqrt{\frac{\mathrm{h}}{\mathrm{m}}}$
  2. $\sqrt{\frac{m}{h}}$
  3. $\sqrt{\frac{h}{p}}$
  4. $\sqrt{\frac{\mathrm{h}}{2(\mathrm{KE})}}$

Solution

$\lambda=\frac{\mathrm{h}}{\mathrm{mv}}$ but $\mathrm{v}=\lambda$
$\therefore \quad \lambda \mathrm{v}=\mathrm{v}^{2}=\frac{\mathrm{h}}{\mathrm{m}}$
$\therefore \quad \mathrm{v}=\sqrt{\frac{\mathrm{h}}{\mathrm{m}}}$ ~

Asked in: JEE-TOPICTESTS-CHEMISTRY

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