In a hydrogen atom,the electron revolves around the nucleus in an orbit of radius $0.53 \times 10^{-10} \, m$. The electrical potential produced by the nucleus at the position of the electron is......$V$

Consider an electron in the $n=3$ orbit of a hydrogen-like atom with atomic number $Z$. At absolute temperature $T$,a neutron having thermal energy $k_B T$ has the same de Broglie wavelength as that of this electron. If this temperature is given by $T = \frac{Z^2 h^2}{\alpha \pi^2 a_0^2 m_N k_B}$,(where $h$ is the Planck's constant,$k_B$ is the Boltzmann constant,$m_N$ is the mass of the neutron and $a_0$ is the first Bohr radius of hydrogen atom),then the value of $\alpha$ is $....$

If the difference between the $(n+1)^{\text{th}}$ Bohr radius and the $n^{\text{th}}$ Bohr radius is equal to the $(n-1)^{\text{th}}$ Bohr radius,then find the value of $n$.

The ratio of radii of $3^{\text{rd}}$ and $6^{\text{th}}$ Bohr's orbit in a hydrogen atom is

In a hydrogen atom,the radius of the $n^{th}$ Bohr orbit is $r_n$. The graph between $\log \left( \frac{r_n}{r_1} \right)$ and $\log n$ will be:

The energy level diagram for a hydrogen-like atom is shown in the figure. The radius of its first Bohr orbit is