We shall present effective approximations measures for certain infinite products related to q-exponential function. There are two main targets. First we shall prove an explicit irrationality measure result for the values of q-exponential function at rational points. Then, if we restrict the approximations to rational numbers of the shape d s /N , we may replace Bundschuh's irrationality exponent 7/3 by 2 + 1 3+2 √ 3 = 2.1547....