For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3V_0$. When the same metal is illuminated by light of wavelength $2\lambda$, then the stopping potential becomes $V_0$. The threshold wavelength for photoelectric emission for the given metal is $\alpha \lambda$. The value of $\alpha$ is ______.

An electromagnetic wave travelling in x-direction is described by field equation

$E_y = 300 \sin \omega \left( t - \frac{x}{c} \right)$.

If the electron is restricted to move in y-direction only with speed of $1.5 \times 10^6$ m/s then ratio of maximum electric and magnetic forces acting on the electron is ______.

Angular momentum of an electron in a hydrogen atom is $\frac{3h}{\pi}$, then the energy of the electron is _____ eV.

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $\alpha \times 10^{-6}$ J. The value of $\alpha$ is _______. (Take surface tension of liquid = 0.08 N/m)