$A$ $100 \ W$ bulb emits light of wavelength '$x$' $\mathring{A}$. What is the value of $x$, if the number of photons emitted is $2.0 \times 10^{20} \ s^{-1}$? $(h = 6.63 \times 10^{-34} \ J \cdot s, c = 3 \times 10^8 \ m \cdot s^{-1})$

Energy of an electron is given by $E = -2.178 \times 10^{-18} \ J \left( \frac{Z^2}{n^2} \right)$. Wavelength of light required to excite an electron in a hydrogen atom from level $n = 1$ to $n = 2$ will be:

According to Bohr's model,the energy of an electron is given by $E = -\frac{2.176 \times 10^{-18}}{n^2} \, J \, atom^{-1}$. Calculate the minimum energy required to remove an electron from the $3^{rd}$ orbit of a $He^{+}$ ion,and also calculate the corresponding wavelength of the photon.

The energy of an electron in the first Bohr orbit of the $H$ atom is $-13.6 \ eV$. The magnitude of the energy value of an electron in the first excited state of $Be^{3+}$ is $.......... \ eV$ $(nearest \ integer \ value)$.

$A$ $25 \ W$ bulb emits monochromatic yellow light of wavelength $0.57 \ \mu m$. Calculate the rate of emission of quanta per second.

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