Threshold frequency f0 = 5.0 x 1014 Hz. If illuminated by incident light of frequency f = 8.1 x 1014 Hz then :-
Work function of metal W = h.f0 = 6.63 x 10-34 x 5 x 1014. = 3.3 x 10-19 J.
Now using kinetic energy = 1/2.m.v2 = h.f - h.f0 which reduces to 2.06 x 10-19 J to find the velocity of the ejected photoelectron.
Hence v2 = (2 x 2.06 x 10 -19)/ 9.11 x 10-31, which calculates to be 6.7 x 105 m.s-1.
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 l1 = h.c/E1 = 122 nm, while l2 = 103 nm and l3 = 98 nm.
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 1014 = 4 x 10-15 eV.s
(b) Threshold frequency read from graph intercept = 2.5 x 1014 Hz
(c) Work Function of the metal = h.f0 = 6.63 x 10-34 x 2.5 x 1014 = 1.65 x 10-19 J.
Using the electron gun velocity formula with accelerating voltage V = 750V
1/2.m.v2 = q.V or v = (2.q.V/m)½ yields v = 1.62 x 107 m.s-1 as the electron velocity.
but the electron de Broglie wavelength (l = h/m.v) = 4.5 x 10-11 m.
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.