X-Ray Diffraction

On a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of \(27.1^{\circ}\) relative to its surface, using an X-ray source of unknown wavelength. Additionally, when illuminated with a different, this time of known wavelength 0.137 nm, a second-order maximum is detected at \(37.3^{\circ}\). Determine (a) the spacing between the reflecting planes, and (b) the unknown wavelength.

Text Transcription:

27.1 degrees

37.3 degrees

Energy Stored in Capacitors U = 1 qV 2 q = CV 1 2 U = CV or 2 1 q2 U = 2 C 37 Energy Density in Capacitors (1) We define the , u, as the electric potential energy per unit volume Taking the ideal case of a parallel plate capacitor that has no fringe field, the volume between the plates is the area of each plate times the distance between the plates, Ad Inserting our formula for the capacitance of a parallel plate capacitor we find 38 Energy Density in Capacitors (2) Recognizing that V/d is the magnitude of the electric field, E, we obtain an expression for the electric potential energy density for parallel plate capacitor This result, which we derived for the parallel plate capacitor, is in fact completely general. This equation holds for all electric fields produced in any way •The formula gives the quantity of electric field energy per unit volume. 39 Example: Isolated Conducting Sphere (1) An isolated conducting sphere whose radius R is 6.85 cm has a charge of q=1.25 nC. Question 1: How much potential energy is stored in the electric field of the charged conductor Answer: Key Idea: An isolated sphere has a capacitance ofC=4πε R (see prev