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The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13?
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The nucleus of an atom can be assumed to be spherical. The radius of t...
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The nucleus of an atom can be assumed to be spherical. The radius of t...
Ans.
Method to Solve :
it is given that radius of nucleus , R = 1.25 � 10-�� A⅓ , where A is mass number.
so, volume of nucleus , V = 4/3 πR�
= 4/3π[ 1.25 � 10-�� 64⅓]�
= 4/3 π[(1.25)� � 10^-39 � 64 ] cm�
given radius of an atom is 1A�
so, volume of atom , v = 4/3πr�
= 4/3 π(10^-8cm)�
= 4/3π[10-�⁴ ] cm�
now, volume of nucleus/volume of atom = (1.25)� � 10^-39 � 64/10^-24
= 125 � 10^-15
= 1.25 � 10-��
hence, answer is 1.25 � 10^-13
so, volume of nucleus , V = 4/3 πR�
= 4/3π[ 1.25 � 10-�� 64⅓]�
= 4/3 π[(1.25)� � 10^-39 � 64 ] cm�
given radius of an atom is 1A�
so, volume of atom , v = 4/3πr�
= 4/3 π(10^-8cm)�
= 4/3π[10-�⁴ ] cm�
now, volume of nucleus/volume of atom = (1.25)� � 10^-39 � 64/10^-24
= 125 � 10^-15
= 1.25 � 10-��
hence, answer is 1.25 � 10^-13
Community Answer
The nucleus of an atom can be assumed to be spherical. The radius of t...
Given:
- Radius of the nucleus, R_nucleus = 1.25 × 10^-13 × A^(1/3) cm
- Radius of the atom, R_atom = 1A
To find:
The fraction of the atomic volume occupied by the nucleus.
Solution:
Step 1: Calculating the volume of the nucleus
The volume of a sphere is given by the formula:
V = (4/3)πr^3
Substituting the given radius of the nucleus, R_nucleus, in the formula:
V_nucleus = (4/3)π(R_nucleus)^3
= (4/3)π(1.25 × 10^-13 × A^(1/3))^3
= (4/3)π(1.25^3 × 10^-13^3 × A)
Step 2: Calculating the volume of the atom
The volume of a sphere is given by the same formula:
V = (4/3)πr^3
Substituting the given radius of the atom, R_atom, in the formula:
V_atom = (4/3)π(R_atom)^3
= (4/3)π(1A)^3
= (4/3)π(1^3)
= (4/3)π
Step 3: Calculating the fraction of the atomic volume occupied by the nucleus
The fraction of the atomic volume occupied by the nucleus is given by the ratio of the volume of the nucleus to the volume of the atom:
Fraction = V_nucleus / V_atom
= [(4/3)π(1.25^3 × 10^-13^3 × A)] / [(4/3)π]
= (1.25^3 × 10^-13^3 × A) / 1
= 1.25^3 × 10^-13^3 × A
= 1.25^3 × 10^-13^3 × 64
= 2.5 × 10^-2
Therefore, the fraction of the atomic volume occupied by the nucleus is 2.5 × 10^-2.
Answer: C) 2.5 × 10^-2
- Radius of the nucleus, R_nucleus = 1.25 × 10^-13 × A^(1/3) cm
- Radius of the atom, R_atom = 1A
To find:
The fraction of the atomic volume occupied by the nucleus.
Solution:
Step 1: Calculating the volume of the nucleus
The volume of a sphere is given by the formula:
V = (4/3)πr^3
Substituting the given radius of the nucleus, R_nucleus, in the formula:
V_nucleus = (4/3)π(R_nucleus)^3
= (4/3)π(1.25 × 10^-13 × A^(1/3))^3
= (4/3)π(1.25^3 × 10^-13^3 × A)
Step 2: Calculating the volume of the atom
The volume of a sphere is given by the same formula:
V = (4/3)πr^3
Substituting the given radius of the atom, R_atom, in the formula:
V_atom = (4/3)π(R_atom)^3
= (4/3)π(1A)^3
= (4/3)π(1^3)
= (4/3)π
Step 3: Calculating the fraction of the atomic volume occupied by the nucleus
The fraction of the atomic volume occupied by the nucleus is given by the ratio of the volume of the nucleus to the volume of the atom:
Fraction = V_nucleus / V_atom
= [(4/3)π(1.25^3 × 10^-13^3 × A)] / [(4/3)π]
= (1.25^3 × 10^-13^3 × A) / 1
= 1.25^3 × 10^-13^3 × A
= 1.25^3 × 10^-13^3 × 64
= 2.5 × 10^-2
Therefore, the fraction of the atomic volume occupied by the nucleus is 2.5 × 10^-2.
Answer: C) 2.5 × 10^-2
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The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13?
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The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13?.
The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The nucleus of an atom can be assumed to be spherical. The radius of the nucleusof mass number A is given as 1.25 ×10^-13×A^(1/3) cm.Radius of atom is 1A. If the mass number is 64,then the fraction of the atomic volume occupied by the nucleus is? A) 1.0×10^-13 B) 5.0 ×10^-5 C)2.5×10^-2 D)1.25 ×10^-13?.
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