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 an electron is 1.813 × 10^–4. Calculate the particle’s mass and identify the particles. Mass of electron = 9.11 × 10 ^–31 kg. 

Answer 1

The de Broglie wavelength λ = h/mv

If λ_e and λ_p are wavelengths of electron and particle respectively, then

= 1.838 × 10³

⇒ m_p = 1.838 × 10³ me

= 1.838 × 10³ × 9.11 × 10^–31

= 1.674 × 10^–27 kg

Which is mass of neutron. Thus the given particle is neutron. The de Broglie wavelength associated with electron is of the same order as the size of electron ; but de Broglie wavelength associated with ball of size 5 mm is too much small than the size of the ball. Hence wave nature of matter is significant in atomic level and insignificant at mascroscopic level.