Question

A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is $1.813\times {10}^{-4}$. The mass of the particle is $(m_e=9.1\times {10}^{-31}kg)$

• A. $1.67\times {10}^{-27}kg$
• B. $1.67\times {10}^{-37}kg$
• C. $1.67\times {10}^{-19}kg$
• D. $1.67\times {10}^{-14}kg$

Answer 1

The correct option is A $1.67\times {10}^{-27}kg$

Given : $\frac{v}{v_e}=3$ and $\frac{\lambda }{{\lambda }_e}=1.813\times {10}^{-4}$

De Broglie wavelength of a moving particle having mass m and velocity v is given by
$\because P=mv=\frac{h}{{\lambda }_D}$

$h=mv{\lambda }_D=m_e{v}_e{\lambda }_{D_e}=mv{\lambda }_D$
Mass of the particle, $m=m_e\left[\frac{{\lambda }_{D_e}}{\lambda }\right]\left[\frac{v_e}{v}\right]$

Substituting the value, we get
$m=9.1\times {10}^{-3}\times \frac{1}{1.813\times {10}^{-4}}\times \frac{1}{3}$

or $m=1.67\times {10}^{-27}kg$