Question

Dual nature of matter was proposed by de Broglie in 1923, it was
experimentally verified by Davisson and Germer by diffraction
experiment. Wave character of matter has significance only for
microscopic particles. de Broglie wavelength or wavelength of
matter wave can be calculated using the following relation:
$\lambda =\frac{h}{mv}$
where, '$m$' and '$v$' are the mass and velocity of the particle.
de Broglie hypothesis suggested that electron waves were being
diffracted by the target, much as $X$-rays are diffracted by planes of
atoms in the crystals.

The wavelength of matter waves associated with a body of mass $1000g$ moving with a velocity of $100m/sec$ is:

• A. $6.62\times {10}^{-39}cm$
• B. $6.62\times {10}^{-36}cm$
• C. $6.626\times {10}^{-36}m$
• D. $3.31\times {10}^{-32}m$

Answer 1

The correct option is C $6.626\times {10}^{-36}m$

$\lambda =\frac{h}{mv}$
$\lambda =\frac{6.626\times {10}^{-27}ergs}{1000g\times 10000cm/s}$
$\lambda =6.626\times {10}^{-34}cm$
$\lambda =6.626\times {10}^{-36}m$
As 1 m$=$ 100 cm.
Thus, the wavelength of matter waves associated with a body of mass 1000 g moving with a velocity of 100 m/sec is $\lambda =6.626\times {10}^{-36}m$.