There are many phenomena in nature that fall off exponentially with some variabl

Question

There are many phenomena in nature that fall off exponentially with some variable. For example, at large distances from the nucleus, an electron cloud in an atom or molecule looks like a fuzzy ball of charge with charge density proportional to e^-alpha r where r is the distance from the nucleus and o is a parameter with units of inverse distance. If curves A and B in the figure at the right represent two such charge distributions, which one has the larger value of alpha? A B They are the same. There is not enough information to tell Explain how you decided For a radioactive material, the number of atoms of a radioactive element decreases like N(t) = N_0e^-t/tau where N_0 is the number of atoms of that element present at time t = 0 and tau is a parameter with units of time representing the time it takes for the number of atoms to decrease by a factor of 1/e. Two radioactive materials start at time t = 0 with the same number of atoms. The graphs at the right show how their numbers fall with time. Which element, A or B, has the larger value of tau? A B They are the same. There is not enough information to tell Explain how you decided

Explanation / Answer

1) D. There is not enough information to tell.

Because, the two curves are coincidning.

at smaller r values B has larger alfa value

at larger r values A has larger alfa value.

2) A. A

because, The no of molecules decreasing rapidly in B comared to A from the graph.

so, time constant of A must greater than B.

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