# 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 $\frac{1}{100}c=\frac{3\times {10}^{8}m/s}{100}=3\times {10}^{6}m/s$

$\lambda =\frac{6.626\times {10}^{-34}J.s}{\left(9.109\times {10}^{-31}kg\right)\left(3\times {10}^{6}m/s\right)}\phantom{\rule{0ex}{0ex}}\lambda =2.43\times {10}^{-10}m\phantom{\rule{0ex}{0ex}}$

Similarly, de- Broglie wavelength associated with ball can be calculated as

$\lambda =\frac{6.626\times {10}^{-34}J.s}{\left(3\times {10}^{-2}kg\right)\left(100m/s\right)}\phantom{\rule{0ex}{0ex}}\lambda =2.2\times {10}^{-34}m\phantom{\rule{0ex}{0ex}}$

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