Question

A cricket ball of 0.5kg is moving with a velocity of \[100m/s\]. The wavelength associated with its motion is:
\[(A). \dfrac{1}{{100}}cm\]
\[(B). 66 \times {10^{ - 34}}m\]
\[(C). 1.32 \times {10^{ - 35}}m\]
\[(D). 6.6 \times {10^{ - 28}}m\]

Answer 1

Hint: As we all know that the de Broglie equation is developed by Louis de Broglie. The de-Broglie derived a connection between the momentum of matter and the wavelength. The de Broglie wavelength is typically inversely proportional to its momentum.
Formula used:
\[\lambda = \dfrac{h}{{mv}}\]

Complete step-by-step solution:
De Broglie wavelength: The de Broglie wavelength is a crucial concept when studying quantum mechanics. The wavelength \[\left( \lambda \right)\] that is related to an object with respect to its speed and mass is called the de Broglie wavelength. A particle de Broglie wavelength is typically inversely proportional to its force.
De Broglie Equation: the wave mechanic postulates that a particle of mass ‘\[m\]’ rotating at a velocity ‘\[v\]’ will have the properties of the wavelength \[\dfrac{h}{{mc}}\] (de Broglie wavelength), where ‘\[h\]’ is the plank constant. We will use the de-Broglie equation to measure the wavelength, momentum, and frequencies or kinetic energy of particles.
Mass: Mass is the amount of matter in an object.
Speed: The speed of an object is the result of a change in its position.
Velocity: Velocity may be a displacement of an object in unit time.
According to the question, the de Broglie wavelength is connected with a ball of mass \[0.5kg\] and moving at a speed of \[100m/s\].
As we all know that the De Broglie equation is;
\[\lambda = \dfrac{h}{{mv}}\]
Where \[\lambda \] is the de Broglie wavelength
\[h\]is the Planck’s constant, \[h = 6.626 \times {10^{ - 34}}Js\]
\[m\] is the mass of the object, \[m = 0.5kg\]
\[v\] is velocity \[v = 100m/s\]
According to the formula of de Broglie equation;
\[\lambda = \dfrac{{6.626 \times {{10}^{ - 34}}}}{{0.5 \times 100}} = 1.32 \times {10^{ - 35}}m\]
\[\lambda = 1.32 \times {10^{ - 35}}m\].
Hence, option C is correct.

Note: The de Broglie equation states that a substance will act like waves, like light and radiation, which also acts correctly as waves and particles. The de Broglie equations concern the wavelength to the momentum ’\[p\]’ and frequency ‘\[f\]’ to the total energy ‘\[E\]’ of a free particle.