The orbital acceleration of an electron in a hydrogen-like atom is given by:

Which of the following statements are true regarding Bohr's model of the hydrogen atom?
$(I)$ Orbiting speed of the electron decreases as it shifts to discrete orbits away from the nucleus.
$(II)$ Radii of allowed orbits of the electron are proportional to the principal quantum number.
$(III)$ Frequency with which the electron orbits around the nucleus in discrete orbits is inversely proportional to the cube of the principal quantum number.
$(IV)$ Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits.
Select the correct answer using the codes given below.

Energy of an electron in an excited hydrogen atom is $-3.4 \text{ eV}$. Its angular momentum will be: $(h = 6.626 \times 10^{-34} \text{ J s})$

An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is $L$. The relation between the magnetic dipole moment $(m)$ associated with it,the gyromagnetic ratio $(R)$,and $L$ is:

The electron in a hydrogen atom is moving in an orbit of radius $0.53 \text{ Å}$. It takes $1.571 \times 10^{-16} \text{ s}$ to complete one revolution. The velocity of the electron will be $[\pi = 3.142]$.

In a hydrogen atom,an electron transitions from an orbit of radius $R$ to an orbit of radius $4R$. What is the ratio of their time periods?