# Chapter 29 - Worked Solutions

### to selected extension questions from the OUP text *Senior Physics -
Concepts in Context* by Walding,
Rapkins and Rossiter

**Q4 :-**
Threshold frequency f_{0} = 5.0 x 10^{14} Hz. If illuminated by incident light of frequency f = 8.1 x 10^{14} Hz then :-

Work function of metal W = h.f_{0} = 6.63 x 10^{-34} x 5 x 10^{14}. = 3.3 x 10^{-19} J.

Now using kinetic energy = 1/2.m.v^{2} = h.f - h.f_{0} which reduces to 2.06 x 10^{-19} J to find the velocity of the ejected photoelectron.

Hence v^{2} = (2 x 2.06 x 10 ^{-19})/ 9.11 x 10^{-31}, which calculates to be 6.7 x 10^{5} m.s^{-1}.

**Q8 :-**
Using the energy level diagram of Figure 29.6 and reconverting the diagram as shown below with the ground state at 0.0 J

The Lyman series of lines in the H - spectrum are ultraviolet photons.

Using E = h.c/l, then l_{1} = h.c/E_{1} = 122 nm, while l_{2} = 103 nm and l_{3} = 98 nm.

**Q25 :-**
The data graphed using an Excel spreadsheet is shown below including a dashed trend line of best fit.. Planck's constant can be calculated as the slope of this line :-

(a) h = slope = (3.0 - 0)/(10 - 2.5) x 10^{14} = 4 x 10^{-15} eV.s

(b) Threshold frequency read from graph intercept = 2.5 x 10^{14} Hz

(c) Work Function of the metal = h.f_{0} = 6.63 x 10^{-34} x 2.5 x 10^{14} = 1.65 x 10^{-19} J.

**Q30 :-**
Using the electron gun velocity formula with accelerating voltage V = 750V

1/2.m.v^{2} = q.V or v = (2.q.V/m)^{½} yields v = 1.62 x 10^{7} m.s^{-1} as the electron velocity.

but the electron de Broglie wavelength (l = h/m.v) = 4.5 x 10^{-11} m.

**Q31 :-**
The energy level diagram is represented below, with appropriate energies of the quantum levels labelled :-

(a) The energy for complete electron detachment or ionization = 8.16 x 10^{-19} J.

(b) The electron is raised to N = 3, three possible photon emissions are labelled on the diagram as level transitions (b), which correspond to values of 3.36 x 10^{-19} J, 4.96 x 10^{-19} J and 1.6 x 10^{-19} J.

(c) Maximum energy = (5.58 x 10^{-19} - 4.96 x 10^{-19}) J = 6.2 x 10^{-20} J.

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