The radius of the third stationary orbit of an electron for a Bohr atom is $R$. The radius of the fourth stationary orbit will be

Find the ratio of the area of the orbit of the first excited state to the ground state in a hydrogen atom.

Ionization potential of a hydrogen atom is $13.6 \text{ eV}$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 \text{ eV}$. According to Bohr's theory,the number of spectral lines emitted by the hydrogen atoms will be:

In the Bohr model of the hydrogen atom,the force on the electron is proportional to which power of the principal quantum number $n$?

Using the formula for the radius of the $n^{th}$ orbit $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$,derive an expression for the total energy of an electron in the $n^{th}$ Bohr orbit.

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 $....$