The dual nature of photons is described by:

Find the radius of the fourth orbit of a hydrogen atom if its radius of the first orbit is $R \text{ pm}$.

Which of the following statements are correct?
$I$) The energy of hydrogen atom in its ground state is $-13.6 \ eV$
$II$) On the basis of Bohr's model,the radius of the $3^{rd}$ orbit of hydrogen atom is $158.7 \ pm$
$III$) The order of radius of the first orbit of $H, He^{+}, Li^{2+}$ and $Be^{3+}$ is $H > He^{+} > Li^{2+} > Be^{3+}$

An electron in a hydrogen atom in its ground state absorbs $2$ times as much energy as the minimum required for it to escape from the atom. The kinetic energy of the emitted electron is ............ $eV$.

$A$ $50 \, W$ bulb emits monochromatic red light of wavelength $795 \, nm$. The number of photons emitted per second by the bulb is $x \times 10^{20}$. The value of $x$ is $......$.
$[ \text{Given} : h=6.63 \times 10^{-34} \, J \cdot s \text{ and } c=3.0 \times 10^{8} \, m \cdot s^{-1} ]$

When a metal surface is irradiated with light of frequency $x \ Hz$,the kinetic energy of emitted photoelectrons is $z \ J$. When the same metal is irradiated with light of frequency $y \ Hz$,the kinetic energy of emitted electrons is $\frac{z}{3} \ J$. What is the threshold frequency (in $Hz$) of the metal?