The material liyf4 is a laser host that crystallizes in the i41/a group. the y site can be substituted with a range of rare-earth ions and sits on the 4b wycoff site. for a rare earth ion with the transition of 4h5/2 to 4g5/2, three peaks are observed at 562, 557 and 553 nm. what are these peaks in cm-1? the first two peaks are strong but the peak at 553 nm is very weak. perform a spin orbit coupling and determine the stark levels and explain these observations. the authors say for transitions of 4h5/2 to a 4f9/2 state there is a strong polarization effect in polarized light. can you justify this from your stark level analysis? what would you expect to see in polarized light? for this problem just use the same approach as you did in 2 above.

A23 kg log of wood begins from rest, 300 m up a sluice (a water track used to transport logs, think of it as an inclined plane with negligible friction) inclined at 20° to the horizontal. after it reaches the flat waterway at the bottom it collides elastically with a 100 kg block of wood initially at rest near the base of the incline. (a) how long does it take the 23 kg log to travel down the incline? (b) what is the speed of the 23 kg log at the bottom of the incline? (c) what are the velocities of both blocks of wood after the collision? (d) what is the total kinetic energy before the collision? (e) what is the kinetic energy of the 23 kg log after the collision? (f) what is the kinetic energy of the 100 kg block of wood after the collision? (g) what is the total kinetic energy after the collision? (h) compare the total initial and total final kinetic energies. is this consistent with what you would expect for elastic collisions? explain!

A2000 kg car is rounding a curve of radius 200 m on a level road. the maximum frictional force the road can exert on the tires of the car is 4000 n. what is the highest speed at which the car can round the curve?

When measuring volume, why is it important to use the correct tools and units to attain the greatest accuracy? use specific examples from the lab to support your answer. (5 points)