Question

A $0.66\,kg$ ball is moving with a speed of $100\,m.{s^{ - 1}}$ . The associated wavelength will be: $(h = 6.6 \times {10^{ - 34}}\,Js)$ .
A. $6.6 \times {10^{ - 32}}\,m$
B. $6.6 \times {10^{ - 34}}\,m$
C. $1 \times {10^{ - 35}}\,m$
D. $1 \times {10^{ - 32}}\,m$

Answer 1

In order to this question, to find the associated wavelength of the movement of ball, we will use de-Broglie’s equation $(\lambda = \dfrac{h}{{mv}})$ that shows the relation between all the mentioned terms in the question, and then we will also discuss about the de-Broglie’s equation.

Complete step by step answer:
The de Broglie equation is one of the equations that is commonly used to define the wave properties of matter. It basically describes the wave nature of the electron. Electromagnetic radiation has the properties of both a particle (with momentum) and a wave (expressed in frequency, wavelength). This dual nature trait was also discovered in microscopic particle-like electrons.

Given that, Mass of the ball, $m = 0.66\,kg$ ,
Velocity of the ball, $v = 100\,m.{s^{ - 1}}$
$h = \text{planck's constant} = 6.6 \times {10^{ - 34}}\,Js$
Now, to find the wavelength, we will use de-Broglie equation that shows the relation between wavelength, mass and the velocity:-
$\lambda = \dfrac{h}{{m.v}}$
where, $\lambda$ is the wavelength, $m$ is the mass of the ball and $v$ is the velocity of the ball.
$\lambda = \dfrac{{6.6 \times {{10}^{ - 34}}}}{{0.66 \times 100}} \\\ \therefore \lambda = 1 \times {10^{ - 35}}\,m \\\$
Hence, the correct option is C.

Note: Every moving particle, according to de Broglie, functions as a wave at times and as a particle at other times. The matter-wave or de Broglie wave, whose wavelength is called the de Broglie wavelength, is related to moving particles.