Single Choice

If the de-Broglie wavelength of a particle of mass $$m$$ is $$100$$ times its velocity then its value in terms of its mass $$(m)$$ and Planck's constant $$(h)$$ is:

A$$\dfrac {1}{10}\sqrt {\dfrac {m}{h}}$$
B$$10\sqrt {\dfrac {h}{m}}$$
Correct Answer
C$$\dfrac {1}{10}\sqrt {\dfrac {h}{m}}$$
D$$10\sqrt {\dfrac {m}{h}}$$

Solution

$$\lambda ={\dfrac {h}{mv}}$$

According to given question $$ \lambda = 100v $$

$$100v={\dfrac {h}{mv}}$$

so $$v^2=\dfrac{h}{100m}$$

$$ \lambda = 100v $$

$$ \lambda= 10 \sqrt {\dfrac{h}{ m}}$$

Hence, the correct option is $$B$$

SIMILAR QUESTIONS

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