Question

Question 5) During the X-ray analysis of an unknown cubic structure, X-ray source with 0.154 nm wavelength is used. The 20 reflection angles are measured as respectively 40, 58, 73, 86.3, 100.4, 114.70 a) What is the kind of the cubic structure? b) What is the lattice constant of this element? c) What do you think this element might be when you consider the periodic table

Answer 1

The answer is attached.

for cubic structure, Also, nd: 2d sind for 1st order diffraction, n=1 . i. >= 2d sino. : from ear and ③ we get, - Sh²+6²+12 :12.4d? sino Pulling value of d , x² = 4a²sino herk²t 12 => sinto = Ch+k+743) Let us call x as common factor (C.f) =) sinto = + kate? WA sing/0.117 = 4²+4² +1². 20 1.. 40 2. 58 3. 73 . 29 . 20 29 36.5 43.15 50.2 57.35 sin²e 0.117 0.235 0.354 0.468 0.590 0,708 2 3 2 N mis wie S. 100.4 114.7 6 Here 0.117 Gwide all is the the common factor sinto values by, 0.117 :

we know that it h +k² + 12 c 1, 2,3,4, 5,6, 3,... then the kind of cubic structure is simple-cubic b) common factor (C.F) 20.117 ? - ya = 2 0 0.117 - 10.154810-92 m2 4a² .117 = 2.372 x 10-20m² 4a² a² = 2.372 x 10-20 m² = 5.93x10 m² 4X0.117 =) o.117 D 7 a² = 5.068 810~20 m² =) a= 2.251 X 1000 m = 2,251 A , .. lattice constant = 2,2514 = 225. 1pm from periodic table with value of lattice constants given we see that the closest value is for fe (Iron) ie. a=b c = 286.65pm Reference - periodic table.com .