The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where $e, h$ and $c$ have their usual meanings).

The maximum wavelength that a sample of hydrogen atoms can absorb is

$A$ particular hydrogen-like ion emits radiation of frequency $3 \times 10^{15} \,Hz$ when it makes a transition from $n=2$ to $n=1$. The frequency of radiation emitted in a transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} \,Hz$, where $X = \text{ . . . . . . }$.

In the Bohr model of the hydrogen atom,the centripetal force is provided by the Coulomb attraction between the proton and the electron. If $r_0$ is the radius of the ground state orbit,$m$ is the mass,$e$ is the charge on the electron,and $\varepsilon_0$ is the permittivity of vacuum,the speed of the electron is:

In the Bohr model of the hydrogen atom,the ratio of the periods of revolution of an electron in $n = 2$ and $n = 1$ orbits is: (in $: 1$)

In a Bohr atom,the total energy of an electron in the $n$-th allowed orbit is $E_n$ and its angular momentum is $J_n$. Then: