Based on a model of fermions which implies a model of photons, a model of the neutron is constructed by merging two photons of equal energy propagating in opposite directions. The fermion model is outlined, and the merging of two photons is described in detail. The radius of the neutron obtained in this way is Rn = 0.84008… fm. This value is four times the reduced Compton wavelength of the neutron. Assuming the same model for the proton, one obtains a value of Rp = 0.84123… fm, which agrees with the most recent experimental value for the charge radius of the proton within the given limits of error. The neutral charge of the neutron is reproduced, and the positive charge of the proton follows within the model, if the proton is formed via the anti-neutron by losing one electron. S = ±ħ/2, and zero dipole moment, is also reproduced for proton and neutron. Further, a value of the magnetic moment of the neutron of μ= &minus2.00μN (μN: nuclear magnetic moment), and of the proton of μ = 2.666… μN is predicted. The deviation by ca. 5% from the recommended respective values of (&minus1.9130μn), and (2.793μn) is ascribed to the (g-2)-anomaly. Finally, the relation of the model with the established description of the nucleons in terms of three quarks bound by gluons is shortly discussed.