Which of the following is the radius of the first orbit of $He^{+}$ (in $pm$)?

The ground and first excited state energies are $E_1$ and $E_2$ respectively. Which pair of species has the same energy? [Note that energy is indicated in the bracket].

The value of Planck's constant is $6.63 \times 10^{-34} \ J \ s$. The speed of light is $3 \times 10^{17} \ nm \ s^{-1}$. Which value is closest to the wavelength in nanometers of a quantum of light with a frequency of $6 \times 10^{18} \ s^{-1}$?

$A$ source of monochromatic radiation of wavelength $400 \, nm$ provides $1000 \, J$ of energy in $10 \, seconds$. When this radiation falls on the surface of sodium,$x \times 10^{20}$ electrons are ejected per second. Assume that wavelength $400 \, nm$ is sufficient for ejection of electrons from the surface of sodium metal. The value of $x$ is $......$. (Nearest integer) $(h = 6.626 \times 10^{-34} \, Js)$

The Balmer series in the hydrogen spectrum corresponds to the transition from $n_1 = 2$ to $n_2 = 3, 4, ...$ This series lies in the visible region. Calculate the wave number of the line associated with the transition in the Balmer series when the electron moves to the $n = 4$ orbit. $(R_H = 109677 \ cm^{-1})$

If $m$ and $e$ are the mass and charge of the revolving electron in the orbit of radius $r$ for a hydrogen atom,the total energy of the revolving electron will be: