A body of mass $10mg$ is moving with a velocity of $100m{s}^{-1}$. The wavelength of the de-Broglie wave associated with it would be (Note:$h=6.63\times {10}^{-34}Js$)

Step1: Given data

A body of mass, $m=10mg$

Velocity, $v=100m/s$

$h=6.63\times {10}^{-34}Js$

Step 2: De-Broglie equation

1. At the subatomic level, quantum mechanics assumes that matter behaves both like a wave and like a particle.
2. According to the De Broglie equation, every moving particle can operate as a wave at times and as a particle at other times. The matter wave, also referred to as the De Broglie wave is a wave that is connected with moving particles.
3. The de Broglie wavelength is the name for the wavelength.

Step3 Formula used

$\lambda =\frac{h}{mv}[where\lambda =de-Brogliewavelength,h=height,m=mass,v=velocity]$

Step4: Calculating the de-Broglie wavelength

$m=10mg=10\times {10}^{-6}kg[As,1mg={10}^{-6}kg]$

Substituting all the given value's in the de-Broglie wavelength formula

$$\begin{gathered} \lambda =\frac{h}{mv} \\ \lambda =\frac{6.63\times {10}^{-34}}{10\times {10}^{-6}\times 100} \\ \lambda =6.626\times {10}^{-31}m \end{gathered}$$

Hence, the wavelength of the de-Broglie wave associated with it would be $6.626\times {10}^{-31}m$.