(a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 13.0 g. Silver has 47 electrons per atom, and its molar mass is 107.87 g/mol. (b) Imagine adding electrons to the pin until the negative charge has the very large value 1.00 mC. How many electrons are added for every 109 electrons already present?
![7. (Poisson Distribution.) Let’s calculate the probability of having n particles in a subvolume V, for a box with total volume KV and a total number of particles T = KN0. (a) Find the exact formula for this probability: n particles in V, with total of T particles in KV. [Hint] What is the probability that the first n particles fall in the subvolume V, and the remainder T - n fall outside the subvolume (K - 1)V? How many ways are there to pick n particles from T total particles? (b) As K → ∞, show that the probability that n particles fall in the subvolume V has the Poisson distribution. What is the mean of this distribution? [Hint] You’ll need to use the fact that e -a = (e -1/K)Ka → (1 - 1/K) Ka as K → ∞, and the fact that n ≪ T. Here don’t assume that n is large: the Poisson distribution is valid even if there are only a few events.](https://www.doubtrix.com/uploads/editor/1022539071bGWWCRzJIA.png)
