Let $R_1$ be the radius of the second stationary orbit and $R_2$ be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $\frac{R_1}{R_2}$ is

In $Li^{++}$ ion,an electron in the first Bohr orbit is excited to a higher energy level by a radiation of wavelength $\lambda$. When the ion de-excites to the ground state in all possible ways (including intermediate emissions),a total of six spectral lines are observed. What is the value of $\lambda$ in $nm$? (Given: $h = 6.63 \times 10^{-34} \, J \cdot s, c = 3 \times 10^8 \, m/s, 1 \, eV = 1.6 \times 10^{-19} \, J$)

The ionization energy of a $Li^{++}$ ion is .......

The ionisation energy of $Li^{2+}$ is equal to

In a hydrogen atom,an electron of mass $9.1 \times 10^{-31} \ kg$ revolves about a proton in a circular orbit of radius $0.53 \ \mathring{A}$. The radial acceleration and angular velocity of the electron are respectively:

If the radius of the first orbit of an $H$ atom is $a_0$, then the de Broglie wavelength of an electron in the third orbit is: (in $\pi a_0$)