$A$ bulb emits light of wavelength $4500 \ \mathring{A}$. The bulb is rated at $150 \ W$ and $8 \ \%$ of the energy is emitted as light. What is the number of photons emitted by the bulb in $1 \ s$?

The values of Planck's constant and the speed of light are $6.63 \times 10^{-34} \ J \ s$ and $3.0 \times 10^8 \ m \ s^{-1}$ respectively. Find the approximate wavelength in nanometers $(nm)$ of a light ray with a frequency of $8 \times 10^{15} \ s^{-1}$.

The longest wavelength of light that can be used for the ionisation of lithium atom $(Li)$ in its ground state is $x \times 10^{-8} \, m$. The value of $x$ is $.....$ (Nearest Integer)
(Given : Energy of the electron in the first shell of the hydrogen atom is $-2.2 \times 10^{-18} \, J$; $h = 6.63 \times 10^{-34} \, Js$ and $c = 3 \times 10^{8} \, ms^{-1}$ )

One energy difference between the states $n = 2$ and $n = 3$ is $E \ eV$,in a hydrogen atom. The ionization potential of the $H$ atom is ............. $E$.

Calculate the radius of the first orbit of $Li^{2+}$. (in $pm$)

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. $(R_H = 109677 \ cm^{-1})$