Question

In: Other

A diffracted x-ray beam is observed from an unknown cubic metal at angles 30.7301 degree, 35.6406...

A diffracted x-ray beam is observed from an unknown cubic metal at angles 30.7301 degree, 35.6406 degree, 51.1984 degree, 60.9706 degree, 64.0327 degree and 75.4344 degree when x-ray of 0.1248 nm wavelength is used.

Determine the indices of the planes (hkl) that produce each of the peaks.

Expert Solution

The formula to determine the indices of the planes using XRD data is,

where, = diffraction angle

= wavelength of X- rays in nm

a = lattice parameter of a crystal in nm

h,k,l = the indices of the peaks

procedure to calculate the indices of the peaks,

1. Calculate for different values of 2

Peak no.	2		1x /	2x/	3x/	hkl
1	30.7301	0.0702
2	35.6406	0.0937
3	51.1984	0.1867
4	60.9706	0.2574
5	64.0327	0.2811
6	75.4344	0.3743

2. Find out the minimum value of (here it is 0.0702) and divide all the values of using this minimum value.Multiply the final result by 1, 2 and 3 and tabulate the results. This is done to get a rounded-off figure for our values.

Peak no.	2			1x /	2x/	3x/	hkl
1	30.7301	0.0702	1	1	2	3
2	35.6406	0.0937	1.3348	1.3348	2.6696	4
3	51.1984	0.1867	2.6595	2.6595	5.319	8
4	60.9706	0.2574	3.6667	3.6667	7.3334	11
5	64.0327	0.2811	4.0043	4.0043	8.0086	12
6	75.4344	0.3743	5.3319	5.3319	10.6638	16

The following values of h,k,l are predetermined indies for specific unit cell systems;

Primitive = 1,2,3,4,5,6,8,9,10,11,12,13,14,16.....

Body-centered = 2,4,6,8,10,12,14,16,....

Face-centered = 3,4,8,11,12,16,19,20,24,27,32,.....

Diamond Cubic = 3,8,11,16,19,24,27,32,....

From the table, 3x/ shows the rounded-off values matching closely with the indices. The indices closely match with the values of Face-centered cubic crystal system. The corresponding h,k,l values of FCC system are listed that would yield the values of .

Peak no.	2			1x /	2x/	3x/		hkl
1	30.7301	0.0702	1	1	2	3	3	111
2	35.6406	0.0937	1.3348	1.3348	2.6696	4	4	200
3	51.1984	0.1867	2.6595	2.6595	5.319	8	8	220
4	60.9706	0.2574	3.6667	3.6667	7.3334	11	11	311
5	64.0327	0.2811	4.0043	4.0043	8.0086	12	12	222
6	75.4344	0.3743	5.3319	5.3319	10.6638	16	16	400

Amanda K answered 6 months ago

A diffracted x-ray beam is observed from an unknown cubic metal at angles 30.7301o, 35.6406o, 51.1984o,...

A diffracted x-ray beam is observed from an unknown cubic metal at angles 30.7301o, 35.6406o, 51.1984o, 60.9706o, 64.0327o and 75.4344o when x-ray of 0.1248 nm wavelength is used. Find the lattice parameter (in nm) of the metal for each of the peaks.

X-ray filter An X-ray beam from a tube with molybdenum anode (?=42) at an acceleration voltage...

X-ray filter An X-ray beam from a tube with molybdenum anode (?=42) at an acceleration voltage of ?=60 kV contains, besides the braking continuum, a distinct ?? peak at 0.71 Å and a smaller ?? peak at 0.63 Å. To filter out the ?? line for diffraction experiments, a zirconium filter (?=40) can be used. Justify this with the help of Mosley's law and draw the X-ray spectrum of molybdenum superimposed with the absorption effect of zirconium. Is the main...

Consider an X-ray beam of wavelength 0.1 nm and a gamma ray beam of wavelength 0.00188...

Consider an X-ray beam of wavelength 0.1 nm and a gamma ray beam of wavelength 0.00188 nm. if each is scattered by an angle of 90 degrees by a free electron, what is the compton shift in the wavelength of the rays? in each case also determine the kinetic energy transferred to the recoiling electron and how much of the incident energy in the rays is lost.

a. Explain why filtering of an X-ray beam causes a simultaneous decrease in beam quantity and...

a. Explain why filtering of an X-ray beam causes a simultaneous decrease in beam quantity and increase in quality [a diagram may be useful] b. The two main mechanisms by which X-rays interact with matter are via Compton scattering and absorption by the photoelectric effect. By referring to the dependence of these effects on X-ray energy, explain what happens to X-ray image quality when using excessively high tube voltages

A beam of x-ray is incident on bone at an intensity of 10 W/m2. Make plot...

A beam of x-ray is incident on bone at an intensity of 10 W/m2. Make plot with your graphics calculator of the intensity as a function of distance through the tissue for energy levels corresponding to : 200 kV, 100 kV, and 50 kV. Draw all curves on the same axis. Repeat this exercise for muscle tissue and compare the results

A 0.046-nm x-ray is incident on a stationary electron. A scattered photon is observed at 94°....

A 0.046-nm x-ray is incident on a stationary electron. A scattered photon is observed at 94°. Find the energy of the scattered photon E'γ= ______ keV and its wavelength λ'= _________ nm Find the kinetic energy of recoiled electron K= _______keV Find the speed of recoiled electron as a fraction of speed of light: v/c= ________

A 0.077-nm x-ray is incident on a stationary electron. A scattered photon is observed at 102°....

A 0.077-nm x-ray is incident on a stationary electron. A scattered photon is observed at 102°. Find the energy of the scattered photon E'γ= keV and its wavelength λ'= nm. Find the kinetic energy of recoiled electron K= keV. Find the speed of recoiled electron as a fraction of speed of light: v/c= .

A third degree polynomial equation (a cubic equation) is of the form p(x) = c3x 3...

A third degree polynomial equation (a cubic equation) is of the form p(x) = c3x 3 + c2x 2 + c1x + c0, where x and the four coefficients are integers for this exercise. Suppose the values of the coefficients c0, c1, c2, and c3have been loaded into registers $t0, $t1, $t2, and $t3, respectively. Suppose the value of x is in $t7. Write the MIPS32 instructions that would evaluate this polynomial, placing the result in $t9.

A beam of wavelength 310 nm from a laser is incident on a metal with work...

A beam of wavelength 310 nm from a laser is incident on a metal with work function 2.7 eV. The power of the laser is 0.15 W. (a) Does the metal emit photoelectrons? Why? (b) What is the range of photoelectron kinetic energies emitted by metal? (c) What is the range of de Broglie wavelengths of these photoelectons? (d) How does result for part (b) change if the laser power is doubled to 0.30 W? Thank you.

In other to achieve higher levels of X-ray attenuation than observed for biological tissue,elements of higher...

In other to achieve higher levels of X-ray attenuation than observed for biological tissue,elements of higher atomic number(Z) are incorporated into the contrast agent molecule. Lithium iodide (LiI) was among the first water-soluble imaging agents. Compare mass attenuation coefficients for soft tissues and for lithium iodide