The figure shows an object and its image formed by a thin lens. Assume that d1 = 0.781 m, d2 = 0.604 m, and h = 7.50E-2 m. What is the image height (in m; answer sign and magnitude)?

Diatomic line. Consider a line of atoms ABAB... AB, with an A-B bond lengtlh of sa. The form factors are fa» fp for atoms A, B, respectively. The incident beam of X-rays is perpendicular to the line of atoms. (a) Show that the interference condition is nd = a cos 0, where 0 is the angle between the diffracted beam and the line of atoms. (b) Show that the intensity of the diffracted beam is proportional to |f, - fB° for n odd, and to |f, + frl° for n even. (c) Explain what happens if fa = fB-

4. Width of diffraction maximum. We suppose that in a linear crystal there are identical point scattering centers at every lattice point pm ger. By analogy with (20), the total scattered radiation amplitude will be proportional to F = E exp[-ima Ak]. The sum over M lattice points is = ma, where m is an inte- 1- exp[-iM(a Ak] 1- exp[-i(a · Ak)] F = by the use of the series 1- xM 1- x M-1 %3D m-0 (a) The scattered intensity is proportional to |F|². Show that sin, M(a · Ak) sin (a · Ak) 2. |F| = F*F = (b) We know that a diffraction maximum appears when a ·Ak = 2th, where h is an integer. We change Ak slightly and define e in a · Ak = 27h + e such that e gives the position of the first zero in sin M(a · Ak). Show that e = 27/M, so that the width of the diffraction maximum is proportional to 1/M and can be extremely narrow for macroscopic values of M. The same result holds true for a three-dimensional crystal.

A first order reflection from the (123) planes of a cubic crystal with the length of the side, a is 687 pm. This reflection was observed at a glancing angle, O when X-rays of wavelength 154 pm were used. (i) Calculate the glancing angle, O.

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The distance between atoms in a molecule is about 10-8 cm . Can visible light be used to “see” molecules?

Crystal lattices can be examined with x rays but not UV. Why?

100mm diameter silicon wafer has 1μm lines fabricated on it. The photomask is made of soda lime glass with a coefficient of thermal expansion (CTE) of 10 ppm (10 × 10−6/ ◦C). How accurately must the temperature in the patterning process be controlled in order to keep distortions from thermal expansion over 100mm wafer below 0.3μm? Silicon CTE is 2.5 × 10−6/ ◦C.

Without stratospheric ozone (O3), harmful solar radiation would cause gene alterations. Ozone forms when the bond in O2 breaks and each O atom reacts with another O2 molecule. It is destroyed by reaction with Cl atoms formed when the C¬Cl bond in synthetic chemicals breaks. Find the wavelengths of light that can break the C¬Cl bond and the bond in O2.

Q. 1. An X-ray beam of wavelength 0.71 A is diffracted by a cubic KCL crystal of density 1.99x10^3 Kgm-3. Calculate the interplanner spacing for (200) planes and glancing angle for the second order reflection from these planes. The molecular weight of KCL is 74.6 amu and the Avagadro’s numberis 6.023x10^26 Kg-1 mole-1.