The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$. What is the radius of the $n = 3$ orbit?

What is the change in angular momentum of an electron in a hydrogen atom when it transitions from the $4^{th}$ orbit to the $5^{th}$ orbit? $(h = 6.6 \times 10^{-34} \, J \cdot s)$

If $E$ and $L$ denote the magnitudes of total energy and of angular momentum of an electron in a Bohr orbit,then the true relation between them is:

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

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:

Ratio of centripetal acceleration for an electron revolving in $3^{\text{rd}}$ and $5^{\text{th}}$ Bohr orbit of hydrogen atom is