What is the ratio of the area of the orbit of an electron in the first excited state to that in the ground state of a hydrogen atom (in $: 1$)?

The electron in a hydrogen atom makes a transition $n_1 \to n_2$,where $n_1$ and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of $n_1$ and $n_2$ are

$A$ diatomic molecule is made of two masses $m_1$ and $m_2$ separated by a distance $r$. Applying the Bohr's quantization rule for angular momentum,calculate its rotational kinetic energy. It is given by the formula:

The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to a transition between these two states,the angular momentum of the electron changes by ($h$ - Planck's constant).

According to Bohr's atomic model,the angular momentum of an electron in the $5^{th}$ orbit of an $H$-atom is:

The de-Broglie wavelength of an electron moving in the $n^{th}$ Bohr orbit of radius $r$ is