(a) (i) Define atomic spectra. (ii) Differentiate between emission spectra and absorption spectra. (b) The diagram above illustrates an electron transition ...

(a)(i) Atomic spectra are the characteristic discrete lines of definite wavelengths or frequencies emitted or absorbed by atoms when electrons move between quantised energy levels.

(a)(ii) An emission spectrum consists of bright lines on a dark background. It is produced when excited electrons fall from higher to lower energy levels, emitting photons. An absorption spectrum consists of dark lines on a bright continuous background. It is produced when atoms absorb photons of particular energies, causing electrons to move from lower to higher energy levels.

(b) Transition from \(n=3\) to \(n=1\)

From the energy-level diagram, \(E_3=-1.51\text{ eV}\) and \(E_1=-13.6\text{ eV}\).

(i) Energy of the photon

\[\Delta E=E_3-E_1=-1.51-(-13.6)=12.09\text{ eV}.\]

\[\Delta E=12.09\times1.6\times10^{-19}=1.934\times10^{-18}\text{ J}.\]

Energy of the photon = \(1.93\times10^{-18}\text{ J}\) \((=12.09\text{ eV})\).

(ii) Frequency of the photon

Using \(E=hf\),

\[f=\frac{E}{h}=\frac{1.934\times10^{-18}}{6.6\times10^{-34}}=2.93\times10^{15}\text{ Hz}.\]

Frequency = \(2.93\times10^{15}\text{ Hz}\).

(iii) Wavelength of the photon

\[\lambda=\frac{c}{f}=\frac{3.0\times10^8}{2.93\times10^{15}}=1.02\times10^{-7}\text{ m}.\]

Wavelength = \(1.02\times10^{-7}\text{ m}\) (about \(102\text{ nm}\)).

(c)(i) Soft X-rays have relatively longer wavelengths, lower frequencies and energies, and low penetrating power. Hard X-rays have shorter wavelengths, higher frequencies and energies, and greater penetrating power.

(c)(ii) Circuit symbol for a p-n junction diode

(c)(iii) A semiconductor is doped to increase the number of charge carriers, thereby increasing its electrical conductivity (or reducing its resistivity).