According to de-Broglie,the de-Broglie wavelength for an electron in an orbit of radius $5.3 \times 10^{-11} \ m$ of a hydrogen atom is $10^{-10} \ m$. The principal quantum number for this electron is:

$A$ proton is fired from a very large distance towards a nucleus with charge $Q = 120e$,where $e$ is the elementary charge. It reaches a distance of closest approach of $10 \ fm$. The de Broglie wavelength of the proton at its initial position is (in $fm$). (Given: mass of proton $m_p = (5/3) \times 10^{-27} \ kg$; $h/e = 4.2 \times 10^{-15} \ J \cdot s/C$; $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$; $1 \ fm = 10^{-15} \ m$)

The energy of $He^{+}$ ion in its first excited state is $......eV$ (The ground state energy for the Hydrogen atom is $-13.6\,eV$).

An electron in a hydrogen atom,after absorbing energy photons,can jump between energy states $n_1$ and $n_2$ $(n_2 > n_1)$. It then returns to the ground state,emitting six different wavelengths in the emission spectrum. The energy of the emitted photons can be equal to,less than,or greater than the absorbed photon energy. Determine $n_1$ and $n_2$.

Which of the following is a property of the Rydberg constant?

The ionization potential for the second $He$ electron is ...... $eV$.