Find the radius of the first,second,and third orbits of the hydrogen atom.

The radius of the second Bohr orbit for hydrogen atom is .......... $\mathring{A}$.
(Planck's constant $h = 6.626 \times 10^{-34} \, Js$; mass of electron $= 9.1091 \times 10^{-31} \, kg$; charge of electron $e = 1.60210 \times 10^{-19} \, C$; permittivity of vacuum $\epsilon_0 = 8.854185 \times 10^{-12} \, C^2 N^{-1} m^{-2}$)

The value of Planck's constant is $6.63 \times 10^{-34} \, J \cdot s$ and the speed of light is $3.0 \times 10^8 \, m \cdot s^{-1}$. The wavelength of a quantum of light with a frequency of $8 \times 10^{15} \, s^{-1}$ is closest to which of the following values in meters?

If the wavelength of an electromagnetic radiation is $2000 \ \text{Å}$, what is its energy in ergs?

The binding energy of an $e^-$ in the ground state of a hydrogen atom is $13.6 \ eV$. The energy required to remove an electron from the ground state of a $He^+$ ion is:

The energy (in $J$) released when an excited electron of the $5^{th}$ orbit of a hydrogen atom returns to its ground state is