A particle moves three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is $1.813 × 10^{-4}$. The mass of the particle is:

$1.67 × 10^{-27} kg$

The correct answer is Option (1) → $1.67 × 10^{-27} kg$

According to De-broglie wavelength,

$λ=\frac{h}{mv}$

and,

$\frac{λ_p}{λ_e}=\frac{m_ev_e}{m_pv_p}=1.813×10^{-4}$

$\frac{m_ev_e}{m_p3v_p}=\frac{m_e}{3m_p}$

$m_p=\frac{m_e}{3×1.813×10^{-4}}=\frac{9.11×10^{-31}}{5.43×10^{-4}}$

$=1.67 × 10^{-27} kg$