Relativistic corrections become necessary when the expression for the kinetic energy $\frac{1}{2}m{v}^2$, becomes comparable with $m{c}^2$, where $m$ is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?

A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values ${\lambda }_1$,${\lambda }_2$ with ${\lambda }_1>{\lambda }_2$ . Which of the following statement are true?

In the explanation of photoelectric effect, we assume one photon of frequency $v$ collides with an electron and transfers its energy. This leads to the equation for the maximum energy $E_{max}$ of the emitted electron as

$E_{max}=hv={\varphi }_0$ where ${\varphi }_0$ is the work function of the metal. If an electron absorbs $2$ photons (each of frequency $v$), what will be the maximum energy for the emitted electron?

In the explanation of photo electric effect, we assume one photon of frequency $v$ collides with an electron and transfers its energy. This leads to the equation for the maximum energy $E_{max}$ of the emitted electron as

$E_{max}=hv={\varphi }_0$ where ${\varphi }_0$ is the work function of the metal. If an electron absorbs $2$ photons (each of frequency $v$), what will be the maximum energy for the emitted electron? Why is this fact (two photon absorption) not taken into consideration in our discussion of the stopping potential?