How Chadwick concluded that the particles are neutrons but not photons? James Chadwick conducted an experiment in which he bombarded Beryllium with alpha particles from the natural radioactive decay of Polonium. How he concluded that the radiation was made up of neutrons and not photons?
 A: The WP article I linked summarizes that

In 1931, Walther Bothe and Herbert Becker found that if alpha particle radiation from polonium fell on beryllium, boron, or lithium, an unusually penetrating radiation was produced. The radiation was not influenced by an electric field, so Bothe and Becker assumed it was gamma radiation. The following year Irène Joliot-Curie and Frédéric Joliot-Curie in Paris showed that if this "gamma" radiation fell on paraffin, or any other hydrogen-containing compound, it ejected protons of very high energy.  Neither Rutherford nor James Chadwick at the Cavendish Laboratory in Cambridge were convinced by the gamma ray interpretation.  Chadwick quickly performed a series of experiments that showed that the new radiation consisted of uncharged particles with about the same mass as the proton.

I boldfaced the crucial observation. High energy means MeVs, and at the time physicists were only familiar with X/γ-ray photons scattering off light electrons relativistically, as in the Compton effect. If you think of electrons as bees, mass-wise, you may think of the proton (the Hydrogen nucleus) as a large billiard  ball, and the Nitrogen  nucleus as a bowling ball, 14 times heavier. So his experiments concluded that the effects of the uncharged projectiles were very energetic, but,  by the high-school physics non-relativistic elastic collision argument below, they obeyed classical physics of a heavy object (at the time!). He estimated its mass to be about that of the proton, the billiard ball, as he says in his paper and his Nobel lecture linked above:

Let us suppose that the radiation consists of particles of mass M moving with velocities up to a maximum velocity V. Then the maximum velocity which can be imparted to a hydrogen atom, mass 1, by the impart of such a particle will be
$$
U_p={2M\over M+1} V
$$
and the maximum velocity imparted to a nitrogen atom will be $$ U_n= {2M\over M+14 }V $$
Then $$\frac{M+14}{M+1}=\frac{U_p}{U_n} $$
The velocities $U_p$ and $U_n$  were found by experiment. The maximum range of the protons ejected from paraffin wax was measured and also the ranges of the recoil atoms produced in an expansion chamber filled with nitrogen. From these ranges the velocities $U_p$ and $U_n$ can be deduced approximately:  $U_p\approx 3.7 \times 10^9$ cm/sec, $U_n\approx  4.7 \times  10^8 $cm/sec. Thus we find M = 0.9. We must conclude that the beryllium radiation does in fact consist of particles, and that these particles have a mass about the same as that of a proton.

The velocities are 1% and 0.1% of the speed of light, respectively, so quite non-relativistic.
The first two formulas are derivable from 9th grade physics, from classical energy & momentum conservation in an elastic billiard-ball to billiard-ball collision, and billiard-ball to bowling ball collision, respectively.
