Answer:
All of the following are already correctly categorized. This facts about these radioactive decays are true. Further, I have explained below in explanation portion.
Step-by-step explanation:
Alpha Decay: Yes it cannot penetrate through paper & Yes it emits Alpha particle when an element undergoes the process of Alpha Decay. Here's how:
First of all, we need to understand why a particular element decays? why radioactive decay occurs?
It is because, everything in this universe tends to achieve its stable state. Everything put efforts to be in their stable state. Likewise, when radioactive elements like Uranium or Thorium become unstable they undergo the process of Alpha decay. As a result, they emit energy and alpha particle.
Furthermore, Alpha decay has low penetration power and it has higher mass than Beta Decay and Gamma Decay that's why it cannot travel in long distances. Hence, it cannot pass through a sheet of paper.
Beta Decay: Yes it emits electrons or positrons and Yes it can penetrate through paper but cannot penetrate through a foil. Here's how:
Till now, we are familiar that why the process of decay occurs right? in order to be stable. Like wise Beta Decay occurs and it emits beta particle and energy. The main difference between alpha decay and beta decay is that alpha particle's mass is much greater than beta particle's mass because beta particle is either a negatively charged electron or positron (a positively charged electron or anti-electron) and we know that mass electron is much smaller.
So, Beta Decay has moderate penetrate power and it's mass is much smaller that's why it can travel in longer distances and it can penetrate paper but cannot penetrate into foil.
Gamma Decay: Yes it requires thick lead shield and yes it emits photon. Here's how:
Gamma Decay is a radioactive wave, it only emits energy in form of photons and it has no mass and no charge and but it has very low wavelength but highest energy with great penetration power and that is the reason that it can penetrate paper, it can penetrate foil but it cannot penetrate thick lead shield.
Hope, this will help :)