In a hydrogen atom in its ground state,the first Bohr orbit has radius $r_1$. When the atom is raised to one of its excited states,the electron's orbital velocity becomes one-third of its initial value. The radius of that orbit is: (in $r_1$)

Suppose in a hypothetical world, the angular momentum is quantized to be even integral multiples of $\frac{h}{2 \pi}$. According to Bohr's model, what will be the largest possible wavelength emitted by hydrogen atoms in the visible range in this world (in $\text{ nm}$)? (Consider $hc = 1242 \text{ eV-nm}$)

Which of the following is a property of the Rydberg constant?

In the Bohr model of the $H$-atom,the kinetic energy of an electron in any orbit depends on the principal quantum number $n$ as:

In hydrogen atoms, the radius of the smallest orbit of the electron is $a_0$. The radius of the third orbit is:

When a hydrogen atom absorbs a photon of wavelength $60 \ nm$,the atom undergoes photo-ionization. What will be the maximum kinetic energy of the emitted electron in $eV$?