An electron of mass m with an initial velocity $$\overrightarrow v = {v_0}\widehat i$$ (v₀ > 0) enters an electric field $$\overrightarrow E = - {\overrightarrow E _0}\widehat i$$ (E₀ = constant > 0) at t = 0. If $$\lambda $$₀ is its de-Broglie wavelength initially, then its de- Broglie wavelength at time t is

When the light of frequency 2$${\upsilon _0}$$ (where $${\upsilon _0}$$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v₁ . When the frequency of the incident radiation is increased to 5$${\upsilon _0}$$ , the maximum velocity of electrons emitted from the same plate is v₂ . The ratio of v₁ to v₂ is

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass m, is

Electrons of mass m with de-Broglie wavelength $$\lambda $$ fall on the target in an X-ray tube. The cutoff wavelength ($$\lambda $$₀) of the emitted X-ray is