In a hydrogen atom, the energy of an electron in the first and third orbits is $E_1$ and $E_3$ respectively. If $E_3 = x E_1$, then the value of $x$ will be:

The total energy of a hydrogen atom in its ground state is $-13.6 \ eV$. If the potential energy in the first excited state is taken as zero,then the total energy in the ground state will be ..... $eV$.

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?

$A$ photon of wavelength $\lambda$ is absorbed by an electron confined to a box of length $L = \sqrt{(35 h \lambda / 8 m c)}$. As a result,the electron makes a transition from state $k=1$ to the state $n$. Subsequently,the electron transitions from the state $n$ to the state $m$ by emitting a photon of wavelength $\lambda^{\prime} = 1.75 \lambda$. Then,

The energy levels for an electron in a certain atom are shown in the figure. Which of the following transitions will emit a photon with the highest energy?

$A$ $12.5 \text{ eV}$ electron beam is used to bombard gaseous hydrogen at ground state. The energy level up to which the hydrogen atoms would be excited is: