A particle moving with a velocity of 270 m/s has the same de Broglie wavelength as an electron moving with a velocity of 6×106 m/s. The mass of the particle is (approximately)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2 × 10−26 kg
The de Broglie wavelength is \( \lambda = h/p = h/mv \). Equal wavelengths mean equal momenta, so Planck’s constant cancels. The electron mass is \( m_e = 9.1\times10^{-31}\,\mathrm{kg} \).
\( \displaystyle \frac{h}{mv} = \frac{h}{m_e v_e} \;\Rightarrow\; mv = m_e v_e \)
\( \displaystyle m = \frac{m_e v_e}{v} \)
\( \displaystyle m = \frac{9.1\times10^{-31}\,\mathrm{kg} \times 6\times10^{6}\,\mathrm{m\,s^{-1}}}{270\,\mathrm{m\,s^{-1}}} \)
\( \displaystyle m = \frac{5.46\times10^{-24}}{270}\,\mathrm{kg} \)
\( m \approx 2.02\times10^{-26}\,\mathrm{kg} \approx 2\times10^{-26}\,\mathrm{kg} \)