To resolve an object in an electron microscope, the wavelength of the electrons must be close to the diameter of the object. what kinetic energy must the electrons have in order to resolve a protein molecule that is 8.80 nm in diameter? take the mass of an electron to be 9.11× 10–31 kg. you should first solve for the velocity of an electron that would have a de broglie wavength equal to the diameter of the protein. then calculate the energy of an electron with this velocity, using the equation for kinetic energy given in the hint below.

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

Aperson walking 1 mile everyday for exercise, leaving her front porch at 9: 00 am and returning to her front porch at 9: 25 am. what is the total displacement of her daily walk? a) 1 mileb) 0c) 25 minutes d) none of the above

Ateacher gives students four liquids commonly found in the kitchen - vinegar, apple juice, dish detergent, and milk - and ph indicator strips, which measure acidity. the teacher asks the students to put the liquids in order from most acidic to most basic. what type of investigation could the students conduct to determine the correct order for the liquids?