In the following atoms and molecules,for the transition from $n = 2$ to $n = 1$,the spectral line of minimum wavelength will be produced by:

Kinetic energy of an electron in one of the orbits of a hydrogen atom is $x$. Then, its total energy is . . . . . . .

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr model to this atom. The longest wavelength photon that will be emitted has wavelength $\lambda$ (given in terms of the Rydberg constant $R$ for the hydrogen atom) equal to:

In $Li^{++}$ ion,an electron in the first Bohr orbit is excited to a higher energy level by a radiation of wavelength $\lambda$. When the ion de-excites to the ground state in all possible ways (including intermediate emissions),a total of six spectral lines are observed. What is the value of $\lambda$ in $nm$? (Given: $h = 6.63 \times 10^{-34} \, J \cdot s, c = 3 \times 10^8 \, m/s, 1 \, eV = 1.6 \times 10^{-19} \, J$)

According to the classical electromagnetic theory,calculate the initial frequency of the light emitted by the electron revolving around a proton in a hydrogen atom.

$A$ muon is an unstable particle with a mass of $207 \, m_e$ and a charge of either $+e$ or $-e$. $A$ muon $(\mu^-)$ is captured by a hydrogen nucleus to form a muonic atom. If the proton captures the $\mu^-$, find the ionization energy of this atom in $keV$.