If the velocity of the electron in Bohr's first orbit is $2.19 \times 10^6 \mathrm{~ms}^{-1}$, calculate the de Broglie wavelength associated with it.

Question

If the velocity of the electron in Bohr's first orbit is $2.19 \times 10^6 \mathrm{~ms}^{-1}$, calculate the de Broglie wavelength associated with it.,

MARKS App · Accepted Answer

$\begin{aligned} \lambda=\frac{\mathrm{h}}{\mathrm{mv}}=& \begin{aligned} & \frac{6.626 \times 10^{-34} \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}}{\left(9.11 \times 10^{-31} \mathrm{~kg}\right)\left(2.19 \times 10^6 \mathrm{~ms}^{-1}\right)} \ &=3.32 \times 10^{-10} \mathrm{~m}=332 \times 10^{-12} \mathrm{~m}=332 \mathrm{pm} \end{aligned} \end{aligned}$

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