Interpretation:
The statement, “Radius
Concept introduction:
The mass of an atom is contained in its nucleus, which is very small and dense.
In the nucleus, the positivelycharged particles are known as protons and the particles that are electrically neutral are known as neutrons.
The Rutherford model of an atom is also called theplanetary model of anatom. It is used to describe the structure of anatom.
The volume of the nucleus is represented by the expression:
A nucleus is spherical in shape. The volume of a sphere is represented by the expression:
The volume of nucleus is calculated as
The nucleus occupies a fraction of the atomic radius is as
Answer to Problem 125AP
Solution:
(a)The statement,“Radius
(b)The volume of the Li nucleus is
(c) The fraction of the atom’s volume is
Explanation of Solution
a)The radius
Nucleons are defined as the sum of the protons and neutrons present in the nucleus of an atom.
The volume of the nucleusis represented by the expression:
A nucleus is spherical in shape. The volume of a sphere is represented by the expression:
Therefore, by equating the expressionsas
Here,
Here,
By equating equation (1) and (2), we get
On solvingfurther, we get
Here,
Therefore, the radius
b) The volume of the Li nucleus.
The radius of the nucleus is
Anucleus hasa spherical shape. The volume of a sphere is to be calculated as
Here,
The volume of nucleus is calculated as
Here,
Substitute the values of the radius and the atomic number in the above expression
Therefore, the volume of the Linucleus is
c) The fraction of atom’s volume is occupied by its nucleus. The results that support the Rutherford model of an atomor not.
The radius of the
The conversion ofpm into m is as
The atomic volume is calculated as
A nucleus has a spherical shape. The volume of a sphere is
Here,
Substitute the values in the above equation
Thus, the atomic volume of lithium is
The nucleus occupies afraction of the atomic radius, which is as follows:
Substitute the values in the above equation
Thus, the fraction of the atom’s volume is
As the nucleus contains a small region in the atom, therefore the results support the Rutherford model of an atom.
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Chapter 2 Solutions
Chemistry
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