The maximum wavelength of light which causes photoelectric emission from photosensitive metal surface is $\lambda_0$. Two light beams of wavelengths $\frac{\lambda_0}{3}$ and $\frac{\lambda_0}{9}$ incident on the metal surface. The ratio of the maximum velocities of the emitted photoelectrons is

A blue lamp emits light of mean wavelength $4500$ Å. The lamp is rated at 150 W and $8 \%$ efficiency. Then, the number of photons are emitted by the lamp per second

If the kinetic energy of a particle in motion is decreased by $36 \%$, the increase in de-Broglie wavelength of the particle is

An electron of mass $m$ with initial velocity $\mathbf{v}=v_0 \hat{\mathbf{i}}\left(v_0>0\right)$ enters in an electric field $\mathbf{E}=-E_0 \hat{\mathbf{i}}$ ( $E_0$ is constant $>0$ ) at $t=0$. If $\lambda$ is its de-Broglie wavelength initially, then the de-Broglie wavelength after time $t$ is