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 kg
B. 0.15 kg
C. 0.2 kg
D. 0.1 kg

Answer 1

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 .

Complete step by step answer:
- 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:
$\begin{aligned} & 6.62\times {{10}^{-35}}=\frac{6.62\times {{10}^{-34}}Js}{x\times 100} \\\ & x=\frac{6.62\times {{10}^{-34}}}{6.62\times {{10}^{-35}}} \\\ & x=0.1kg \\\ \end{aligned}$
Hence, we can conclude that the correct option is (D), that is the mass of the body is 0.1 kg.

Additional Information:
- It was de Broglie who found that the matter can also show the wave particle duality, just like the light. As light can behave like both of the particles and as a wave.
- And he also reasoned that matter would also follow the same equation for wavelength as light.

Note:
- We should not forget to write units after solving any question.
- We can say that de Broglie concept is most important, which is used to construct microscopes that are used in the measurement of objects of very small size.