Let p be the density 2(2) - 1/2 exp(- x2 ) (x > 0) of the modulus x = lzl of a standard normal variate

Let p be the density 2(2π)^-1/2 exp(-½^x2) (x > 0) of the modulus x = lzl of a standard normal variate z and let q be the density β^-1 exp(-x/β) (x > 0) of an E(β) distribution. Find the value of β such that q is as close an approximation top as possible in the sense that the Kullback-Leibler divergence (q : p) is a minimum.