Calculate the de-Broglie wavelength of an electron moving with a speed of 1/100 of the speed of light in vaccum and the ball of radius 5 mm and mass 3*10^-2 kg moving with a speed of 100 m/s

 

 Dear Student,

Please find below the solution to the asked query:

The de-Broglie wavelength $\lambda$associated with matter can be given as

$\lambda =\frac{h}{mv}$
Where, h is Planck's constant, m is mass of the particle and v is the speed of particle.

Planck's constant h = 6.626 x 10 ^-34 J-s
Mass of electron  m_e = 9.109 x 10^-31 kg
Electron is moving with $\frac{1}{100}c=\frac{3\times {10}^8 m/s}{100}= 3\times {10}^6 m/s$
 

Thus, de- Broglie wavelength associated with electron can be calculated as
$$\begin{gathered} \lambda =\frac{6.626\times {10}^{-34}J.s}{\left(9.109\times {10}^{-31}kg\right)\left(3\times {10}^{6}m/s\right)} \\ \lambda =2.43\times {10}^{-10}m \end{gathered}$$
Similarly, de- Broglie wavelength associated with ball can be calculated as

$$\begin{gathered} \lambda =\frac{6.626\times {10}^{-34}J.s}{\left(3\times {10}^{-2}kg\right)\left(100 m/s\right)} \\ \lambda =2.2\times {10}^{-34}m \end{gathered}$$

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