The electronic transitions from $n=2$ to $n=1$ will produce the shortest wavelength in which of the following species? (where $n$ is the principal quantum state)

Rutherford created a theoretical picture of the atom based on :

$A$ certain metal has a work function of $\Phi = 2 \ eV$. It is irradiated first with $1 \ W$ of $400 \ nm$ light and later with $1 \ W$ of $800 \ nm$ light. Among the following,the correct statement is
[Given: Planck constant $(h) = 6.626 \times 10^{-34} \ J \ s$;
Speed of light $(c) = 3 \times 10^8 \ m \ s^{-1}$ ]

The energy of an electron in the first Bohr orbit of $H$ atom is $-13.6 \ eV$. The possible energy value$(s)$ of the excited state$(s)$ for electrons in Bohr orbits of the hydrogen atom is(are) $............ \ eV$.

The ratio of ground state energy of $Li^{2+}$,$He^{+}$,and $H$ is:

In the spectrum of $Li^{2+}$,the difference between two energy levels is $2$ and their sum is $4$. Find the wavelength of the photon emitted during the transition between these two energy states.