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What will be the wavelength of a ball of mass $0.1kg$ moving with a velocity of $10m{s^{ - 1}}$ ?

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Last updated date: 22nd Jul 2024
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Answer
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Hint: We have to know that de Broglie frequency is a significant idea while contemplating quantum mechanics. The wavelength that is related to an article corresponding to its force and mass is known as de Broglie frequency. A molecule's de Broglie frequency is typically conversely corresponding to its power.

Complete answer:
We have to see, it is said that matter has a double nature of wave-particles. de Broglie waves, named after the pioneer Louis de Broglie, are the property of a material article that fluctuates on schedule or space while carrying on also to waves. It is additionally called matter waves. It holds extraordinary comparability to the double idea of light which carries on as molecule, and wave, which has been demonstrated tentatively.
When de Broglie contemplated that matter likewise can show wave-molecule duality, actually like light, since light can act both as a wave (it tends to be diffracted and it has a frequency) and as a molecule. And furthermore contemplated that matter would follow a similar condition for frequency as light to be specific,
$\lambda = \dfrac{h}{p}$ (or) $\lambda = \dfrac{h}{{mv}}$
Where,
$p$ = linear momentum $\left( {mv} \right)$ ,
$h$ = Planck constant = $6.626 \times {10^{ - 34}}Js$ ,
$m$ = mass
$v$ = velocity.
In the given details,
Mass of ball ( $m$ ) = $0.1kg$ ,
Velocity of ball ( $v$ ) = $10m{s^{ - 1}}$ ,
By using the above de Broglie equation,
$\lambda = \dfrac{h}{{mv}} = \dfrac{{6.626 \times {{10}^{ - 34}}Js}}{{(0.1Kg) \times 10m{s^{ - 1}}}} = 6.626 \times {10^{ - 34}}m$ .
Hence, $6.626 \times {10^{ - 34}}m$ is the answer.

Note:
We have to know that, the articles which we find in everyday life have frequencies that are exceptionally little and undetectable, thus, we don't encounter them as waves. Be that as it may, de Broglie frequencies are very noticeable on account of subatomic particles.