Which of the following has the largest de Bro | vedclass

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(D) The de Broglie wavelength is given by the formula $\lambda = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass,and $v$ is the velocity.

Vedclass · Accepted Answer

$A$ ball of mass $0.03 \ kg$ moving with speed $1 \ m/s$

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(D) The de Broglie wavelength is given by the formula $\lambda = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass,and $v$ is the velocity.Since $\lambda \propto \frac{1}{mv}$,the particle with the smallest momentum $(mv)$ will have the largest de Broglie wavelength.Calculating momentum $(p = mv)$ for each case:$A$: $p = 0.02 \ kg 	imes 1000 \ m/s = 20 \ kg \cdot m/s$$B$: $p = 0.06 \ kg 	imes 10 \ m/s = 0.6 \ kg \cdot m/s$$C$: $p = 0.01 \ kg 	imes 100 \ m/s = 1 \ kg \cdot m/s$$D$: $p = 0.03 \ kg 	imes 1 \ m/s = 0.03 \ kg \cdot m/s$Comparing the values,the momentum in option $D$ is the smallest $(0.03 \ kg \cdot m/s)$.Therefore,the ball in option $D$ has the largest de Broglie wavelength.

Which of the following has the largest de Broglie wavelength?

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