(a) Explain the terms:
(i) transmutation as it relates to radioactivity; (ii) stopping potential.
(b) \(^{23}_{11}A + ^2_1B\) —> \(^p_qC\) + proton
\(^p_qC\) —> \(^r_sE\) + beta
A nucleus C, formed artificially from A and B radioactive and quickly decays to another nucli E as indicated in the nuclear equations abc Datermine the values of p, q, r and s.
(c) A certain metal of work function 1.6 eV is irradiated with ultra-violet light of wavelength 3.6 x 10\(^{-7}\) Calculate the maximum
(i) kinetic energy of ejected electron in joules;
(ii) speed of an emitted electron. (1eV = 1.6 x 10\(^{-18}\) J; C = 3.0 x 10\(^{8}\) ms\(^{-1}\); m, = 9.1 x 10\(^{-31}\) kg; h = 6.6 x 10\(^{-34}\) Js)
(d) If source of the ultra-violet light in (c) above is mo away from the surface of the metal, state the of on the maximum speed of the ejected electron
Explanation
(a)(i) Transmutation is the change of one chemical element into another by radioactive disintegration or nuclear bombardment with particles. Example is the conversion of mercury to gold.
(ii) Stopping potential is the p.d of the anode of a photocell with respect to the cathode at which no electrons will reach the anode stopping potential Vs
= \(\frac{ht}{e} - \frac{Wo}{e}\)
(b) \(^{23}_{11}A + ^2_1B + ^1_1P\)
P + 1 = 23 + 2
P = 24
q + 1 = 11 + 1
q = 11
\(^{24}_{11}C \to ^r_sE + ^o_{-1}B\)
r + 0 = 24; r = 24
S - 1 = 11; S = 12
(c) (i) W = 1.6eV = 1.6 x 1.6 x 10\(^{-19}\)
= 2.56 x 10\(^{-19}\)J
E = \(\frac{hc}{\lambda} = \frac{6.6 \times 10{-34} \times 3 \times 10^{8}}{3.6 \times 10^{-7}}\)
E = W + K.E\(_{max}\)
ii) K.E = \(\frac{1}{2}mv^2\)
2.94 x 10\(^{-19}\) = \(\frac{1}{2} \times 9 \times 10^{-3} \times V^2_{max}\)
V\(_{max} = 8.04 \times 10^5 m/s\)
(d) No effect.