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Matter Waves

The uncertain...

Question

The uncertainty in position of a particle is same as it's de Broglie wavelength, uncertainty in its momentum is _______

A

\frac{h}{λ}

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B

\frac{λ}{h}

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C

\frac{2 h}{3 λ}

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D

\frac{3 λ}{2 h}

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Solution

The correct option is A $\frac{h}{λ}$
$Δ x = λ$ $(\frac{a}{q})$
According to the Uncertainty principle,
$Δ x \cdot Δ p \geq \frac{h}{4 π}$
$∴ Δ p \geq \frac{1}{4 π} (\frac{h}{λ}) ∴ Δ p \propto \frac{h}{λ}$

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The French physicist Louis de Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behaviour. He proposed the following relationship between the wavelengh

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