Question

If radius of the ${}_{13}A{{l}^{27}}$ nucleus is estimated to be $3.6fermi$, then the radius of ${}_{52}T{{e}^{125}}$ nucleus nearly
(A) 6 fermi
(B) 8 fermi
(C) 4 fermi
(D) 5 fermi

Answer 1

Hint: We know that the nucleus is a collection of particles called protons, which are positively charged, and neutrons, which are electrically neutral. Protons and neutrons are in turn made up of particles called quarks. The chemical element of an atom is determined by the number of protons, or the atomic number, Z, of the nucleus. Most of the mass in an atom resides in the nucleus. electrons. The charge Z of the nucleus then determines the number of the electrons in the atom and is the only property of the nucleus of importance for atomic physics, and consequently for most of the properties of matter as we know it.

Complete step-by step answer:
It is known that together, the number of protons and the number of neutrons determine an element's mass number: mass number is given as protons added to neutrons. If we want to calculate how many neutrons an atom has, we can simply subtract the number of protons, or atomic number, from the mass number.
We know that radius of a nucleus, $R={{R}_{0}}{{A}^{\dfrac{1}{3}}}$
Where, ${{R}_{0}}$ is a constant and A is a mass number.
Now for $AIR={{R}_{0}}{{(27)}^{\dfrac{1}{3}}}$
So, we have to evaluate $Te,R'={{R}_{0}}{{(125)}^{\dfrac{1}{3}}}$
On solving both the above equations, $R'=6fermi$.
Therefore, the radius of ${}_{52}T{{e}^{125}}$ nucleus nearly $6fermi$.

Hence, the correct answer is Option A.

Note: We know that atomic mass is the weighted average mass of an atom of an element based on the relative natural abundance of that element's isotopes. The mass number is a count of the total number of protons and neutrons in an atom's nucleus. The mass number of an atom is its total number of protons and neutrons. Atoms of different elements usually have different mass numbers, but they can be the same. For example, the mass number of argon atoms and calcium atoms can both be 40.
On the other hand, the atomic number or proton number having a symbol Z of a chemical element is the number of protons found in the nucleus of every atom of that element. The atomic number uniquely identifies a chemical element. It is identical to the charge number of the nucleus.