The de-Broglie wavelength associated with a particle of mass $m$ moving with velocity $v$ is:

An electron in an electron microscope with initial velocity $v_{0} \hat{i}$ enters a region of a stray transverse electric field $E_{0} \hat{j}$. The time taken for the change in its de-Broglie wavelength from the initial value of $\lambda$ to $\lambda / 3$ is proportional to

Consider two particles of different masses. In which of the following situations will the heavier of the two particles have a smaller de-Broglie wavelength?

The $log-log$ graph between the energy $E$ of an electron and its de-Broglie wavelength $\lambda$ will be

The de Broglie wavelength of an oxygen molecule at $27^{\circ} C$ is $x \times 10^{-12} \ m$. The value of $x$ is (take Planck's constant $= 6.63 \times 10^{-34} \ J \cdot s$, Boltzmann constant $= 1.38 \times 10^{-23} \ J/K$, mass of oxygen molecule $= 5.31 \times 10^{-26} \ kg$).

Let $E_e$ and $E_p$ represent the kinetic energy of an electron and a photon,respectively. If the de-Broglie wavelength of a photon is twice the de-Broglie wavelength of an electron,then find the ratio $E_p / E_e$. (Given: speed of electron $v = c / 100$,where $c$ is the velocity of light).