Chapter 2

Consider the hydrogen atom to be a proton embedded in a cavity of radius \(a_{0}\) (Bohr radius) whose charge is neutralised by the addition of an electron to the cavity in vacuum, infinitely slowly. Estimate the average total energy of an electron in its ground state in a hydrogen atom as the work done in the above neutralisation process. Also, if the magnitude of the average kinetic energy is half the magnitude of the average potential energy, find the average potential energy.

Iodine molecule dissociates into atoms after absorbing light of \(4500 \AA\). If one quantum of radiation is absorbed by each molecule, calculate the kinetic energy of iodine atoms. (Bond energy of \(\left.\mathrm{I}_{2}=240 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)\)

Find out the number of waves made by a Bohr electron in one complete revolution in its 3rd orbit.

What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition \(n=4\) to \(n=2\) of \(\mathrm{He}^{+}\)spectrum?

Estimate the difference in energy between Ist and 2nd Bohr orbit for a hydrogen atom. At what minimum atomic number, a transition from \(n=2\) to \(n=1\) energy level would result in the emission of \(X\)-rays with \(\lambda=3.0 \times 10^{-8} \mathrm{~m} ?\) Which hydrogen atom-like species does this atomic number correspond to ?

The electron energy in hydrogen atom is given by \(E=\left(-21.7 \times 10^{-12}\right) / n^{2}\) ergs. Calculate the energy required to remove an electron completely from the \(n=2\) orbit. What is the longest wavelength (in \(\mathrm{cm}\) ) of light that can be used to cause this transition?

Naturally occurring boron consists of two isotopes whose atomic weights are \(10.01\) and \(11.01\). The atomic weight of natural boron is \(10.81\). Calculate the percentage of each isotope in natural boron.