The particles in an atmosphere will not escape the gravitational pull of a celestial body if their velocity is smaller than 1/6 the escape velocity of the celestial body. the escape velocity is dependent on the mass (m) and radius (r) of the celestial body. the interactive allows you to select from multiple planets to see how the escape velocity would increase as the mass and radius of the celestial body increase. select a temperature of 1000 k for mercury, then play the simulation. as you will see, all of the particles will escape the atmosphere. let's pick one particle, h20, and try to estimate how much larger the mass of mercury would need to be to retain water at this temperature. the escape velocity vesc is proportional to (mr).the interactive tells us that venus can retain water at these temperatures, so we can use its mass-to-radius ratio to solve for the new mass of mercury required to retain h20. using the mass and radius of venus as a reference and assuming the radius of mercury is constant at ∼0.38r. earth, determine approximately how large the mass would need to be?

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.

In positive numbers less than 1, the zeros between the decimal point and a non-zero number are blank significant

Which type of basaltic lava flow has a fairly smooth