The energy levels for a hydrogen-like species with atomic number $Z$ can be given by:

If the wavelength of the first line of the Balmer series is $656.1 \ nm$,then the wavelength of the second line of this series will be ............. $nm$.

$A$ bulb emits electromagnetic radiation of $660 \, nm$ wavelength. The total energy of radiation is $3 \times 10^{-18} \, J$. The number of emitted photons will be :
$(h = 6.6 \times 10^{-34} \, J \cdot s, \, c = 3 \times 10^{8} \, m/s)$

In Rutherford's experiment,generally the thin foil of heavy atoms,like gold,platinum etc. have been used to be bombarded by the $\alpha$-particles. If the thin foil of light atoms like aluminium etc. is used,what difference would be observed from the above results?

The value of Planck's constant is $6.63 \times 10^{-34} \, J \cdot s$ and the speed of light is $3.0 \times 10^8 \, m \cdot s^{-1}$. The wavelength of a quantum of light with a frequency of $8 \times 10^{15} \, s^{-1}$ is closest to which of the following values in meters?

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