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 de Broglie wavelength is given by:
λ = h / (mv).
Given that the particle moves three times as fast as an electron and the wavelength ratio is 1.813 × 10-4, we use the relation:
λparticle / λelectron = melectronvelectron / (mparticlevparticle).
Substituting values and solving for mass, we get:
mparticle ≈ 1.67 × 10-27 kg.
Thus, the correct answer is (a).
Important Questions from Dual Nature of Radiation and Matter
A point source causing photoelectric emission from a metallic plate is moved away from the plate. The variation of photoelectric current with distance from the source is correctly represented by the graph:
The wavelength of light from the spectral emission line of sodium is 662 nm. The kinetic energy at which an electron would have the same de Broglie wavelength would be: (h=6.62×10−34J⋅s,me=9×10−31kg)
Energy of a photon corresponding to a wavelength of 600 nm is 2.08 eV. The energy of a photon of wavelength 400 nm will be:
According to Einstein’s photoelectric equation, the plot of the Kinetic Energy of the emitted photoelectrons from a metal versus the frequency of the incident radiation gives a straight line whose slope:
Energy of a photon corresponding to a wavelength of 600 nm is 2.08 eV. The energy of a photon of wavelength 400 nm will be:
