The spectrum of the CMB looks like a blackbody with a temperature
   T = 2.73 Kelvin.

      Q:  What is the wavelength of the peak of this spectrum?



        The spectrum of a blackbody has a peak wavelength related
        to temperature in the following manner:

                          0.002898 m * K 
            lambda  =   --------------------
                              T (Kelvin)


        So, plugging in the temperature T = 2.73 Kelvin


                          0.002898 m * K
            lambda  =    -------------------  =  0.00106 m  =  1.06 mm
                              2.73 K