How many photons are required to provide $1 \, J$ of energy with a wavelength of $5000 \, \mathring{A}$?

In astronomical observations,signals observed from the distant stars are generally weak. If the photon detector receives a total of $3.15 \times 10^{-18} \, J$ from the radiations of $600 \, nm$,calculate the number of photons received by the detector.

The distance between the $3^{rd}$ and $2^{nd}$ Bohr's orbits in the hydrogen atom is

The ratio of the slopes of the $KE_{max}$ vs $v$ and $V_0$ vs $v$ curves in the photoelectric effect gives ($v$ is the frequency of incident radiation and $V_0$ is the stopping potential).

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:

When an electron in a hydrogen atom jumps from an infinite state to the first stationary state,the wavelength of the emitted radiation will be ...... (Rydberg constant = $1.097 \times 10^7 \ m^{-1}$):