For a hydrogen atom with $n = 1$,the radius of the Bohr orbit is approximately $0.530 \, \mathring{A}$. What will be the radius for the first excited state $(n = 2)$ in $\mathring{A}$?

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 $H > He^{+} > Li^{2+} > Be^{3+}$

When an electron in a hydrogen spectrum transitions from the $7^{th}$ energy level to the $1^{st}$ energy level,what is the total number of spectral lines produced?

Four lowest energy levels of $H$-atom are shown in the figure. The number of emission lines could be obtained by transitions from these levels. The total number of possible emission lines is:

$A$ photon of wavelength $3000 \ \mathring{A}$ strikes a metal surface. The work function of the metal is $2.13 \ eV$. What is the kinetic energy of the emitted photoelectron (in $eV$)? $\left(h=6.626 \times 10^{-34} \ J \ s\right)$

The value of Rydberg constant $\left(R_H\right)$ is $2.18 \times 10^{-18} \ J$. The velocity of an electron having mass $9.1 \times 10^{-31} \ kg$ in Bohr's first orbit of a hydrogen atom $= \dots \dots \dots \times 10^5 \ ms^{-1}$ (nearest integer).