(a) A helium lamp is used for an experiment to study thephotoelectric effect. The visible part of the spectrum emitted fromthe lamp is split into its components using a glass prism, whichreveals a yellow spectral line at 587nm and a blue spectral line at447nm.

(i) Explain briefly the origin of the distinct lines ofdifferent colour.

(ii) Has blue or yellow light higher energy (per photon)?Justify your answer.

(iii) The refractive index of the glass prism is larger for bluelight than for yellow. Will the direction of blue or yellow lightchange by a larger angle compared to the incident light? Justifyyour answer.

(iv) Has blue or yellow light higher velocity within the glassprism? Justify your answer.

(b) The yellow light and blue light from part (a) hit a piece ofpotassium with work function 2.29 eV.

(i) Calculate the energy of the emitted photoelectrons.

(ii) Electrons are fermions. State the difference betweenfermions and bosons in terms of their spin quantum number.

(iii) Briefly explain the meaning of the Pauli exclusionprinciple.

(iv) A helium ion with total charge −e has 3 electrons. Showthat there are four different combinations of spin magnetic quantumnumber that these electrons can have. Justify your answer on thebasis of the aufbau principle.