Question

# A body of mass x kg is moving with the velocity of $100\text{ }m\text{ }{{\sec }^{-1}}$ . Its de Broglie wavelength is$6.62\times {{10}^{-35}}m$. Hence x is:$\left[ h=6.62\times {{10}^{-34}}J-\sec \right]$A. 0.25 kgB. 0.15 kgC. 0.2 kgD. 0.1 kg

Hint: It is found that de Broglie wavelength is associated with an object, in relation to its mass and momentum. de Broglie equation for wavelength is given by the formula: $\lambda =\frac{h}{mv}$
Where, $\lambda$is the wavelength, h is the plank constant, m is the mass of the body and v is the velocity .

- We are being provided with the value of wavelength $\lambda$ =$6.62\times {{10}^{-35}}m$
velocity is$100\text{ }m\text{ }{{\sec }^{-1}}$ and $\left[ h=6.62\times {{10}^{-34}}J-\sec \right]$
- We will find the mass of the body as x.
- As we know that de Broglie equation for wavelength is given by the formula $\lambda =\frac{h}{mv}$
So, by putting all the values given, in the formula we get:
\begin{align} & 6.62\times {{10}^{-35}}=\frac{6.62\times {{10}^{-34}}Js}{x\times 100} \\ & x=\frac{6.62\times {{10}^{-34}}}{6.62\times {{10}^{-35}}} \\ & x=0.1kg \\ \end{align}
Hence, we can conclude that the correct option is (D), that is the mass of the body is 0.1 kg.