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

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.