The observation of the line spectrum of the hydrogen atom indicates that

The ground state energy of hydrogen atom is $-13.6 \ eV$. The energy of the second excited state of $He^{+}$ ion in $eV$ is:

Heat treatment of muscular pain involves radiation of wavelength of about $900 \ nm$. Which spectral line of $H$ atom is suitable for this purpose?
$[R_H = 1.097 \times 10^7 \ m^{-1}, \ h = 6.626 \times 10^{-34} \ J \cdot s, \ c = 3 \times 10^8 \ m/s]$

Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has the duration of $2 \, ns$ and the number of photons emitted during the pulse source is $2.5 \times 10^{15}$,calculate the energy of the source.

What is the work function of the metal if the light of wavelength $4000 \, \mathring{A}$ generates photoelectrons of velocity $6 \times 10^5 \, ms^{-1}$ from it? ............. $eV$ (Mass of electron $= 9 \times 10^{-31} \, kg$; Velocity of light $= 3 \times 10^8 \, ms^{-1}$; Planck's constant $= 6.626 \times 10^{-34} \, Js$; Charge of electron $= 1.6 \times 10^{-19} \, C \, eV^{-1}$)

An electronic transition in a hydrogen atom results in the formation of the $H_\alpha$ line of the hydrogen spectrum in the Lyman series. The energies associated with the electron in each of the orbits involved in the transition (in $kcal \ mol^{-1}$) are: