(a) Write Einstein’s photoelectric equation and identh: each component of the equation.
(b) For a photocell, star; one factor each that is responsible fo: the:
(i) emission (ii) rate of emission;
(iii) energy of photoelectrons.
(c)(i) Two nuclear equations are given below:
(^{222}_{p}RN) (to) (^{218}_{84}PO + ^q_2He)……………….A
(^{214}_{83}RN) (to) (^{214}_{84}PO + ^m_nX)……………….B
Determine the values of: ((alpha)) p and q in equation A; ((beta)) in and n in equation B and identify X.
(ii) Give a reason why it is important to dispose o radioactive waste safely.
(d)(i) A certain atom emits ultra violet photon of wavelength 2.4 x10(^{-7})m. Calculate the energy of the photon:
—————– – 6.0 x 10(^{-19})J
—————- – 8.2 x 10(^{-19})J
—————- – 8.8 x 10(^{-19})J
—————- – 16.7 x 10(^{-19})J
(ii) The figure above illustrates the energy levels o the atom. Copy the figure in your answer booklet anc indicate on it, the energy level transitions which cause the emission of the photon in (d)(i) above. [h= 6.6 x 10(^{-34}) Js; c = 3.0 x 108 ms(^{-1})].
Explanation
(a) Einstein’s photoelectric equation is
E = W + K Emax, where
E = Energy of incident radiation
W = Work function
K.E(_{text{max}}) = Maximum kinetic energy of photoelectron.
(b) For photocell factors responsible for:
(i) Emission (to) frequency or wavelength of incident radiation.
(ii) Rate of emission (to) intensity of incident radiation or number of photons.
(iii) Energy of photoelectrons —> frequency or wavelength of incident radiation.
(c)(i) ((alpha)) 218 + q = 222
q = 4
((alpha)) P = 84 + 2 = 86,
m = 214 — 214 = 0
n = 83 — 84 = —1
x is an electron or beta particle.
ii) Needs to safely dispose radioactive waste:
(1) it emits harmful radiations.
(2) it is toxic
(d)(i) E = (frac{hc}{lambda})
= (frac{6.6 times 10^{-34} times 3.0 times 10^{8}}{2.4 times 10^{8}})
= 8.25 x 10(^{-19})J
(ii)
E(_4) —————– – 6.0 x 10(^{-19})J
E(_3) —————- – 8.2 x 10(^{-19})J
E(_2) —————- – 8.8 x 10(^{-19})J
E(_1) —————- – 16.7 x 10(^{-19})J
The energy level transitions which cause the emission of the photon in (d)(i) is. E(_3)