The density of the electron states in a metal can be written as g(E) = AE^(1/2), where is a constant and is measured from the bottom of the conduction band.
Derive the total number of states in this material and calculate the fraction of conduction electrons ƒ within KT of the Fermi energy for molybdenum at 300 K. Hints: Use the approximation (1- KT/Eꜰ)^(3/2) ≈ 1-(3/2)KT Eꜰ^(1/2).
Calculate the Fermi energy for this metal at 0 K using the expression for the density of electron states. Assume the electronic structure contains 1 electron per atom.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min

conservation of mass

mass before something happens = mass afterwards