The de-Broglie wavelength $\lambda$ associated with an electron having kinetic energy $E$ is given by the expression:

The graph which shows the variation of the de Broglie wavelength $(\lambda)$ of a particle and its associated momentum $(p)$ is

An electron of mass $m_{e}$ and a proton of mass $m_{p}$ are moving with the same speed. The ratio of their de-Broglie's wavelengths $\lambda_{e} / \lambda_{p}$ is

Choose the only correct statement out of the following:

The kinetic energy of an electron and a proton is $10^{-32} \ J$. Then the relation between their de-Broglie wavelengths is

$A$ charged particle $q_0$ of mass $m_0$ is projected along the $y-$axis at $t = 0$ from the origin with a velocity $v_0$. If a uniform electric field $E_0$ also exists along the $x-$axis,then the time at which the de Broglie wavelength of the particle becomes half of its initial value is: