This problem examines the number of energy states available in the conduction band that are very close to the band edge Ec. a. Using the formula below for the density of energy states per unit volume, perform the integral from the bottom of the conduction band (Ec) to an energy band 1.2kT above the edge and determine the number of states available per cm³. N(E) d E=\frac{\sqrt{2}}{\pi^{2}}\left(\frac{m_{n}{ }^{*}}{\hbar^{2}}\right)^{3 / 2} \sqrt{E} d E b. Compare your result to the effective density of states in the conduction band for silicon at room temperature (300K) given by the formula N_{c}=2\left(\frac{2 \pi m_{n}^{*} k_{B} T}{h^{2}}\right)^{3 / 2} C. Compare your result to the number of silicon atoms per cm³ you calculated HW1 and determine the ratio of the number of energy states/cm³ to the number of silicon atoms/cm³ and comment.