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:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $1.67 × 10^{-27} kg$
According to De-broglie wavelength,
$λ=\frac{h}{mv}$
and,
$\frac{λ_p}{λ_e}=\frac{m_ev_e}{m_pv_p}=1.813×10^{-4}$
$\frac{m_ev_e}{m_p3v_p}=\frac{m_e}{3m_p}$
$m_p=\frac{m_e}{3×1.813×10^{-4}}=\frac{9.11×10^{-31}}{5.43×10^{-4}}$
$=1.67 × 10^{-27} kg$