For an electron moving in the $n^{\text{th}}$ Bohr orbit,the de Broglie wavelength of the electron is:

In the Bohr model of a hydrogen-like atom,the force between the nucleus and the electron is modified as $F = \frac{e^2}{4\pi \varepsilon_0} \left( \frac{1}{r^2} + \frac{\beta}{r^3} \right)$,where $\beta$ is a constant. For this atom,the radius of the $n^{th}$ orbit in terms of the Bohr radius $\left( a_0 = \frac{\varepsilon_0 h^2}{m \pi e^2} \right)$ is:

The total energy of an electron $E_n = -\frac{Z^2me^4}{8\epsilon_0^2n^2h^2}$ in an atom is based on which hypothesis? Under what condition is this formula true?

De-Broglie wavelength of an electron orbiting in the $n=2$ state of a hydrogen atom is close to (Given Bohr radius $= 0.052 \ nm$) (in $nm$)

Magnetic field at the centre of the hydrogen atom due to the motion of an electron in the $n^{\text{th}}$ orbit is proportional to:

When a hydrogen atom is in its first excited level,its radius is .... of the Bohr radius.