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  4. If the uncertainty in the position of a particle is equal to its de-Broglie wavelength, the minimum uncertainty in its velocity should be

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Q. If the uncertainty in the position of a particle is equal to its de-Broglie wavelength, the minimum uncertainty in its velocity should be

NTA AbhyasNTA Abhyas 2022

Solution:

$\Delta x.m.∆v\geq \frac{h}{4 \pi }$
or $\lambda .m.∆v\geq \frac{h}{4 \pi }$
or $\frac{h}{m v}m.∆v\geq \frac{h}{4 \pi }$
or $\Delta v\geq \frac{v}{4 \pi }$