An electron of a hydrogen atom in an excited state has an energy $E_n = -0.85 \ eV$. The maximum number of allowed transitions to lower energy levels is:

In the third orbit of a hydrogen atom,the energy of an electron is $E$. In the fifth orbit of a helium ion $(Z=2)$,the energy of an electron will be:

The following diagram indicates the energy levels of a certain atom. When the system moves from the $2E$ level to the $E$ level, it emits a photon of wavelength $\lambda$. What is the wavelength of the photon produced during its transition from the $\frac{4E}{3}$ level to the $E$ level?

$A$ sample of hydrogen atoms is in an excited state (all the atoms). The photons emitted from this sample are made to pass through a filter through which light having a wavelength greater than $800 \ nm$ can only pass. Only one type of photon is found to pass through the filter. The sample's initial excited state is: [Take $hc = 1240 \ eV \cdot nm$,ground state energy of hydrogen atom = $-13.6 \ eV$.]

An electron in the $n = 1$ orbit of a hydrogen atom is bound by $13.6 \, eV$. If a hydrogen atom is in the $n = 3$ state,how much energy is required to ionize it?

The number of spectral lines emitted by atomic hydrogen that is in the $4^{\text{th}}$ energy level is