4. (Problems on Shell Theorems) Assume the following model of the proton. It consists of: 1) a solid spherical core having a radius 1/10 the radius of the proton; 2) a concentric hollow spherical shell with no charge; and 3) a concentric solid spherical shell which has an inner radius exactly 1/2 the radius of the proton, and an outer radius that of the radius of the proton. (The hollow spherical shell is situated in between the solid spherical core and the shell.) Assume the charge of the core is exactly half of the total charge of the proton and that charge is distributed uniformly on both the core and the solid spherical shell. What is the force (in Newtons) due to the proton on a small object having a charge equal to the charge of the electron and which is at the following distance from the center of the proton: a) exactly two proton radii; b) 1/2 the radius of the proton; c) at the surface of the core; d) zero (i.e. at the center of the proton). Hint: use the shell theorems for electricity. The radius of the proton is about 0.840.87 fm.
Radioactive decay
The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. This periodic table's elements come in a variety of shapes and sizes. Several of these kinds are stable like nitrogen-14, hydrogen-2, and potassium-40, whereas others are not like uranium-238. In nature, one of the most stable phases of an element is usually the most prevalent. Every element, meanwhile, has an unstable state. Unstable variants are radioactive and release ionizing radiation. Certain elements, including uranium, have no stable forms and are constantly radioactive. Radionuclides are elements that release ionizing radiation.
Artificial Radioactivity
The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.
4. (Problems on Shell Theorems) Assume the following model of the proton. It consists of: 1) a solid spherical core having a radius 1/10 the radius of the proton; 2) a concentric hollow spherical shell with no charge; and 3) a concentric solid spherical shell which has an inner radius exactly 1/2 the radius of the proton, and an outer radius that of the radius of the proton. (The hollow spherical shell is situated in between the solid spherical core and the shell.) Assume the charge of the core is exactly half of the total charge of the proton and that charge is distributed uniformly on both the core and the solid spherical shell. What is the force (in Newtons) due to the proton on a small object having a charge equal to the charge of the electron and which is at the following distance from the center of the proton: a) exactly two proton radii; b) 1/2 the radius of the proton; c) at the surface of the core; d) zero (i.e. at the center of the proton). Hint: use the shell theorems for electricity. The radius of the proton is about 0.840.87 fm.
The shell theorems state-
(i) the electric field inside a uniform shell of charge is zero
(ii) that the field outside the uniform shell of charge is the same as that of a point charge with the same total charge as the shell.
Here, Given data
Radius of proton (R) = 0.84087 fm
(here, in given question, radius of the proton is about 0.840.87 fm. The value doesn't make any sense.)
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