Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6 \mathring{A}$. The radius of the third Bohr orbit of $He^{+}$ is $..................$ picometer. (Nearest Integer)

Find the ionization energy and the wavelength of the photon emitted for a hydrogen atom transition from $n_1 = 2$ to $n_2 = \infty$.

$A$ single-electron species has a nuclear charge of $+Ze$,where $Z$ is a constant. The energy required to excite an electron from the $2^{nd}$ Bohr orbit to the $3^{rd}$ Bohr orbit is $47.2 \ eV$. Calculate the value of $Z$.

The wavelength of a particular electron transition for $He^{+}$ is $100 \ nm$. The wavelength (in $\mathring{A}$) of $H$ atom for the same transition is

In an electron transition from an infinite state to the ground state in an $H$ atom,find the emitted wavelength. (in $nm$)

If the shortest wavelength of the Lyman series of the $H$ atom is $x$,then calculate the total energy of the $H$ atom in the first excited state.