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Q. According to de Broglie concept, all material particles posses wave character as well as particle character. The wave associated with a moving particle is called matter wave. The wavelength of the matter wave is given by the equation
$\lambda=\frac{ h }{ p }=\frac{ h }{ mv }$ where $p$ is the momentum of the particle, $'m$ ' is the mass of the particle and ' $v$ ' is the velocity of the particle. 'h' is called Planck's constant.
The wavelength associated with an electron (mass = $9.11 \times 10^{-31} kg$ ) moving with a velocity of $10^{6} m s ^{-1}$ is $\left( h =6.625 \times 10^{-34} J\, s \right)$

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Solution:

$\lambda=\frac{ h }{ mv }$
$=\frac{6.625 \times 10^{-34}}{9.11 \times 10^{-31} \times 10^{6}}$ meter
$=\frac{6.625}{9.11} \times 10^{-9}$ meter
$=0.727 \times 10^{-9}$ metre
$=0.727\, nm$