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The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom?
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The unit of length convenient on the nuclear scale is a fermi: 1 f = 1...
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The unit of length convenient on the nuclear scale is a fermi: 1 f = 1...
Understanding Nuclear Density
The empirical relation for nuclear radius is given by:
r = r0 * A^(1/3)
where r0 is approximately 1.2 fermi (1.2 x 10^-15 m), and A is the mass number.
Implication of the Relation
- Volume of the Nucleus:
The volume V of a nucleus can be expressed as:
V = (4/3)πr^3
Substituting the expression for r, we get:
V ∝ A
- Mass of the Nucleus:
The mass of a nucleus is roughly equal to its mass number in atomic mass units (u). Thus, for a nucleus with mass number A, the mass m = A u.
- Density of the Nucleus:
Density ρ is given by:
ρ = mass/volume
Since both mass and volume are proportional to A, the density remains nearly constant across different nuclei.
Estimating Sodium Nucleus Density
- Mass Number (A) of Sodium:
Sodium has a mass number A = 23.
- Calculating Volume:
Using r0 = 1.2 fermi:
r = 1.2 * 23^(1/3) fermi ≈ 3.7 fermi
Converting to meters:
r ≈ 3.7 x 10^-15 m
Volume V ≈ (4/3)π(3.7 x 10^-15 m)^3 ≈ 2.1 x 10^-45 m^3
- Mass of Sodium Nucleus:
Mass m ≈ 23 u ≈ 23 x 1.66 x 10^-27 kg ≈ 3.82 x 10^-26 kg
- Density Calculation:
Density ρ ≈ m/V ≈ (3.82 x 10^-26 kg) / (2.1 x 10^-45 m^3) ≈ 1.82 x 10^17 kg/m^3.
Comparison with Sodium Atom Density
- Average Atomic Density of Sodium:
The average density of a sodium atom is about 0.97 g/cm^3 or 970 kg/m^3.
- Observations:
The density of the sodium nucleus (1.82 x 10^17 kg/m^3) is vastly greater than the average atomic density (970 kg/m^3). The significant difference highlights that nuclear densities are uniform and extremely high compared to the more spacious atomic structure.
The empirical relation for nuclear radius is given by:
r = r0 * A^(1/3)
where r0 is approximately 1.2 fermi (1.2 x 10^-15 m), and A is the mass number.
Implication of the Relation
- Volume of the Nucleus:
The volume V of a nucleus can be expressed as:
V = (4/3)πr^3
Substituting the expression for r, we get:
V ∝ A
- Mass of the Nucleus:
The mass of a nucleus is roughly equal to its mass number in atomic mass units (u). Thus, for a nucleus with mass number A, the mass m = A u.
- Density of the Nucleus:
Density ρ is given by:
ρ = mass/volume
Since both mass and volume are proportional to A, the density remains nearly constant across different nuclei.
Estimating Sodium Nucleus Density
- Mass Number (A) of Sodium:
Sodium has a mass number A = 23.
- Calculating Volume:
Using r0 = 1.2 fermi:
r = 1.2 * 23^(1/3) fermi ≈ 3.7 fermi
Converting to meters:
r ≈ 3.7 x 10^-15 m
Volume V ≈ (4/3)π(3.7 x 10^-15 m)^3 ≈ 2.1 x 10^-45 m^3
- Mass of Sodium Nucleus:
Mass m ≈ 23 u ≈ 23 x 1.66 x 10^-27 kg ≈ 3.82 x 10^-26 kg
- Density Calculation:
Density ρ ≈ m/V ≈ (3.82 x 10^-26 kg) / (2.1 x 10^-45 m^3) ≈ 1.82 x 10^17 kg/m^3.
Comparison with Sodium Atom Density
- Average Atomic Density of Sodium:
The average density of a sodium atom is about 0.97 g/cm^3 or 970 kg/m^3.
- Observations:
The density of the sodium nucleus (1.82 x 10^17 kg/m^3) is vastly greater than the average atomic density (970 kg/m^3). The significant difference highlights that nuclear densities are uniform and extremely high compared to the more spacious atomic structure.
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The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom?
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The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom?.
The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The unit of length convenient on the nuclear scale is a fermi: 1 f = 10^-15m. Nuclear sizes obey roughly the following empirical relation:r=r0A^1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom?.
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