(a)(i) State the principal factor that determines the relative stability of a radioactive nucleus.

(ii) Arrange the following radioactive nucleus in decreasing order of stability. Justify your answer: X,W and Y: 

\(^40{X}_20\)   \(^920{Y}_36\) and \(^95{Z}_42\)

(b)(i) Explain the term ionization potential.
(ii)

The diagram above illustrates energy levels  in the hydrogen atom. E, is the energy of the E\(_0\) ground state.

(i) When an electron makes a transition from level n = 3 to level n = 1, it emits a photon of wavelength 1.02x 10\(^{-7}\)m. Calculate E\(_0\).

(ii) Calculate the ionization potential of the hydrogen atom.

(c)(i) Explain the statement, the work function of sodium is 2.0 eV. (ii) Light of wavelength 160 mm is shone on the surface of a sodium metal of work function 2.0 eV. Determine whether photoelectrons will be emitted. [h = 6.6 x 10\(^{-34}\) Js, e = 3.0 x 10\(^{8}\)m/s, I eV = 1.6 x 10\(^{-19}\) J]