Question

The α-particles with 6.7 MeV kinetic energy are directed into a gold plate. The thickness of the gold plate is 3.4x10-7 m, the number of cores per unit volume of the plate is 5.9x1028 cores / m ^ 3, and the number of α-particles hitting the gold plate per second is 4.1x107.
a) Find the fraction of α-particles scattered between 30 ° and 60 °.
b) The window of an α-detector placed at a 45 ° deviation angle at a distance of 15 cm from the point of collision of the bundle is 4 cm2. Find the number of α-particles coming to the detector for 30 minutes.

dedektör r O > parçacığı lehva (Au)

Answer 1

Date Page No. o do A Solgt since tortot 9 a particles Anatom Nuclencs betector beam d5= (arrsing) Xorda parameter = Then According to figure Impact effective or scattering enous section Rb2 Now if the thickness of the gold foil is t an atom in per unit Valedon n then Number of scattered particle fraction nt to=ntap? know that tot % are fi we ze? न where Then f of 072 E tu kinetic energy of the E nt a ze? 4 t folt 2 22 et 16 st 2 60 ²612 a - nta 2 2

Then df = ntr z² el 16 T² Gold Cotize coser?@ do (by differentiation ) alson ds [ds = an angle af ang sinco de 4517? Sinan Cordo (from the figure differential area of detector which particles In are detected at X Number of incident x-particle If the is number Ni then of particles scattered at an angle a No of Nitas from the NIO) NA Atst z²e4 Ni af ds equation 0 and ☺ cot to corecho de 16026682 4002 sine case de 22 e 209 cosec ecte Mito Nontz 6436² € 21 22 2 Z Rutherford scattering formula. Hence Mitas cosector

Dato Page No. @ N(30°) cose coseet Go sint 30 379415 3 (asmis cor150g? 2, sintiso 16 cost 15° T3.928 te Given ( = 6:7 Mev 6 = 67x16x26x1019 t = To:72 x6135 30 4 x 10 m -7 5 gxto 3 n Z o 79 450 15cm = 0.15 m no. of particles hitting the gold per second Pence Nos of incident partido disting, the time intervale Bomin 1800 selon tence No. of incident particles so 4: 2 X 107 X 18 0 = 73.8 X10 g 4. q Xeo7 Nion = Henre No. of par Ades coming to defector in zogain af at 45° angle =

N145) cofecre Nintzen 1672602 G282 2 (73-8x109) 15.9x108% (39407) (7972 X16Xolgge cosecta 76x43-1912x68-459tzāl2727 720-72315138 X (6.152 18, 9 306112 xot 1. 893612 X107