Chapter 1

Hydrogen possesses three isotopes, but tritium \(\left(^{3} \mathrm{H}\right),\) which is radioactive, occurs as less than 1 in \(10^{17}\) atoms in a sample of natural hydrogen. If the value of \(A_{\mathrm{r}}\) for hydrogen is 1.008 , estimate the percentage abundance of protium, \(^{1} \mathrm{H}\), and deuterium, \(^{2} \mathrm{H}\) (or \(\mathrm{D}\) ) present in a sample of natural hydrogen. Point out any assumptions that you make. Explain why your answers are not the same as those quoted in Appendix 5.

State which of the following \(n^{\prime}-n\) transitions in the emission spectrum of atomic hydrogen belong to the Balmer, Lyman or Paschen series: (a) \(3 \rightarrow 1 ;\) (b) \(3-2\) (c) \(4--3\) (d) \(4--2\) (e) \(5-1\)

Calculate the energy (in kJ per mole of photons) of a spectroscopic transition, the corresponding wavelength of which is \(450 \mathrm{nm}\).

Using the Bohr model, determine the values of the radii of the second and third orbits of the hydrogen atom.

How is the (a) energy and (b) size of an \(n s\) atomic orbital affected by an increase in \(n ?\)

Write down a set of quantum numbers that uniquely defines each of the following atomic orbitals: (a) \(6 s\) (b) each of the five \(4 d\) orbitals.

Do the three \(4 p\) atomic orbitals possess the same or different values of (a) principal quantum number, (b) the orbital quantum number and (c) the magnetic quantum number? Write down a set of quantum numbers for each \(4 p\) atomic orbital to illustrate your answer.

How many radial nodes does each of the following orbitals (a) \(2 s ;(b) 4 s ;(c) 3 p ;(d) 5 d\) possess: \(l ;\) (e) \(1 s ;(f) 4 p ?\)

Comment on differences between plots of \(R(r)\) against \(r\) and \(4 \pi r^{2} R(r)^{2}\) against \(r\) for each of the following atomic orbitals of an \(\mathrm{H}\) atom: (a) \(1 s ;\) (b) \(4 s ;\) (c) \(3 p\).

Write down the sets of quantum numbers that define the (a) \(1 s,\) (b) \(4 s,\) (c) \(5 s\) atomic orbitals.