(a) In 1932 James Chadwick observed emission of neutral radiation when beryllium nuclei were bombarded with alpha-particles. It was found that this neutral radiation could knock out protons from light nuclei such as those of helium, carbon and nitrogen. The only neutral radiation known at that time was photons. Application of the principles of conservation of energy and momentum showed that if the neutral radiation consisted of photons, the energy of photons would have to be much higher than is available from the bombardment of beryllium nuclei with alpha-particles. So, Chadwick assumed that the neutral radiation consists of a new type of neutral particles called neutrons.
(b) Radius of nucleus depends on the total number of neutrons and protons.
Let assume one nucleus has n1 neutrons and p1 protons. The second nucleus has n2 neutrons and p2 protons. If
n1+p1=n2+p2
then the radius of the two nuclei will be equal even though they are having different number of neutrons and different number of protons.