(a) (i) What is nuclear fission?
(ii) State the function of each of the following ma-terials in a nuclear fision reactor:
((alpha)) graphite, ((beta)) boron rods; ((gamma)) liquid sodium
(b) The table below gives some of the energy levels of a hydrogen atom.
| n | 1 | 2 | 3 | 4 | 5 | (infty) |
| E(_n)/_eV) | -13.60 | -3.39 | -1.51 | -0.85 | -0.54 | 0.00 |
(i) Draw the energy level diagram for the atom.
(ii) Determine the wavelength of the photon emitted when the atom goes from the energy state n = 3 to the ground state. [h = 6.6 x 10(^{-34}) Js, c = 3 x 10(^{8})ms(^{-1}), e = 1.6 x 10(^{-19})]
(c) A piece of ancient bone from an excavation site showed (^{14}_{6})C activity of 9.5 disintegrations per minute per 1.0×10(^{-3})kg. If a bone specimen from a living creature shows (^{14}_{6})C activity of 12.0 disintegrations per minute per 1.0 x 1 0(^{-3}), determine the age of the ancient bone. [Half – life of (^{14}_{6})C = 5572 years].
Explanation
(a)(i) Nuclear Fission is the splitting up of a heavy nucleus into lighter nuclei with release of a huge amount of energy and neutrons.
(ii) ((alpha)) graphite; ((beta)) Boron rods; ((gamma) )Liquid sodium
|
Material |
Function |
|
Graphite |
Slows down high energetic neutrons in the reaction chamber. |
|
Boron rods |
To absorb excess neutrons so as to control fission rate |
|
Liquid sodium |
Extraction / conduction of excess heat from the reaction chamber. |
(b)(i) E(_n), n = (alpha) ———————————- 0.eV
E(_4), n = 5 —————————————————- – 0.54eV
E(_3), n = 4 —————————————————- – 0.85eV
E(_2), n = 3 —————————————————- 1.51eV
E(_1), n = 2 —————————————————— 3.39eV
(ii) Using (lambda) = (frac{hc}{Delta E})
= (frac{6.6 times 10^{-34} times 3.0 times 10^8}{(-1.51 – ( – 13.60)) times 1.6 times 10^{-19}})
= 1.02 x 10(^{-7})m
(c) (lambda) = (frac{0.693}{ T^{frac{1}{2}}}) = (frac{0.693}{5572})
= 0.0001244 years(^{-1})
N = Noe(^{- lambda t})
e(^{0.0001244t}) = 1.2632
0.0001244t = 0.234
t = 1878 years