The de Broglie wavelength of an electron revolving in the first Bohr orbit of circumference $2\pi r$ is ............

In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is:

If $m$ is the mass of an electron,$v$ is its velocity,$r$ is the radius of a stationary circular orbit around a nucleus with charge $Ze$,then from Bohr's first postulate,the kinetic energy of the electron is (where $K = 1 / 4 \pi \epsilon_0$):

When the electron orbiting in a hydrogen atom in its ground state moves to the third excited state,the de-Broglie wavelength associated with it

When an electron in a hydrogen atom is excited from its $4^{th}$ to $5^{th}$ stationary orbit,the change in angular momentum of the electron is (Planck's constant: $h = 6.6 \times 10^{-34} \ J \cdot s$)

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text{th}}$ energy state by emitting a photon of energy $2.86 \ eV$. The integer value of $n$ will be . . . . . . .