Suppose an electron in an atom experiences an attractive force towards the nucleus given by $F = k/r$,where $k$ is a constant and $r$ is the distance of the electron from the nucleus. Applying the Bohr model to this system,the radius of the $n^{th}$ orbit $r_n$ and the kinetic energy of the electron in that orbit $K_n$ are found. Which of the following relationships is correct?

The ratio of the kinetic energy to the total energy of an electron in a Bohr orbit is

In a mixture of $H-He^{+}$ gas ($He^{+}$ is a singly ionized $He$ atom),$H$ atoms and $He^{+}$ ions are excited to their respective first excited states. Subsequently,$H$ atoms transfer their total excitation energy to $He^{+}$ ions by collisions. Assume that the Bohr model of the atom is exactly valid.
$1.$ The quantum number $n$ of the state finally populated in $He^{+}$ ions is
$(A) 2$ $(B) 3$ $(C) 4$ $(D) 5$
$2.$ The wavelength of light emitted in the visible region by $He^{+}$ ions after collisions with $H$ atoms is
$(A) 6.5 \times 10^{-7} \ m$ $(B) 5.6 \times 10^{-7} \ m$ $(C) 4.8 \times 10^{-7} \ m$ $(D) 4.0 \times 10^{-7} \ m$
$3.$ The ratio of the kinetic energy of the $n=2$ electron for the $H$ atom to that of the $He^{+}$ ion is
$(A) 1/4$ $(B) 1/2$ $(C) 1$ $(D) 2$

When an electron jumps from the orbit $n=2$ to $n=4$,the wavelength of the radiation absorbed will be ($R$ is Rydberg's constant).

The wavelengths involved in the spectrum of deuterium $(_1^2D)$ are slightly different from that of hydrogen spectrum,because

Angular momentum of an electron in a hydrogen atom is $\frac{3h}{2\pi}$. The wavelength of this electron is approximately $...... \mathring{A}$.