The $Cs^+$ ion imparts a violet color to the flame. How is this related to the emitted radiation?

Calculate the energy of one mole of photons of radiation whose frequency is $5 \times 10^{14} \ Hz$.

The wavelength range of the visible spectrum extends from violet $(400 \, nm)$ to red $(750 \, nm).$ Express these wavelengths in frequencies $(Hz).$ $(1 \, nm = 10^{-9} \, m)$

The photoelectric effect is described as the ejection of electrons from the surface of a metal when :

When electromagnetic radiation of wavelength $300 \, nm$ falls on the surface of a metal, electrons are emitted with a kinetic energy of $1.68 \times 10^5 \, J \, mol^{-1}$. What is the minimum energy (work function) needed to remove one mole of electrons from the metal? $(h = 6.626 \times 10^{-34} \, J \, s, c = 3 \times 10^8 \, m \, s^{-1}, N_A = 6.022 \times 10^{23} \, mol^{-1})$

$A$ photon of $300 \, nm$ is absorbed by a gas and then re-emits two photons. One re-emitted photon has a wavelength of $496 \, nm$. The wavelength of the second re-emitted photon is: (in $, nm$)