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 $1.813\times {10}^{-4}.$ Calculate the particle’s mass. (Given mass of electron is $9.109\times {10}^{-31}kg)$

• A. $1.675\times {10}^{-27}kg$
• B. $9.109\times {10}^{-31}kg$
• C. $9.109\times {10}^{-27}kg$
• D. $1.675\times {10}^{-31}kg$

Answer 1

The correct option is A $1.675\times {10}^{-27}kg$

Given, $v_P=3v_e$
de Broglie wavelength is given by
$\lambda =\frac{h}{p}=\frac{h}{mv}$
From the question, $\frac{{\lambda }_P}{{\lambda }_e}=1.813\times {10}^{-4}$
$\Rightarrow \frac{m_e{v}_e}{m_P\left(3v_e\right)}=1.813\times {10}^{-4}$
$\Rightarrow m_P=\frac{m_e}{5.439\times {10}^{-4}}=\frac{9.109\times {10}^{-31}}{5.439\times {10}^{-4}}$
$=1.675\times {10}^{-27}kg$