Textbook Question
Use the mass spectrum of mercury to estimate the atomic mass of mercury. Estimate the masses and percent intensity values from the graph to three significant figures.
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Ch.2 - Atoms & Elements
Chapter 2, Problem 107a
Carbon-12 contains six protons and six neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers). Calculate the volume of the nucleus and the volume of the atom.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Nuclear Volume Calculation
The volume of a nucleus can be estimated using the formula for the volume of a sphere, V = (4/3)πr³, where r is the radius of the nucleus. For Carbon-12, with a radius of approximately 2.7 femtometers, this formula allows us to calculate the nuclear volume, which is significantly smaller than that of the entire atom.
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00:59
Effective Nuclear Charge Calculation
Atomic Volume Calculation
Similarly, the volume of an atom is calculated using the same spherical volume formula, but with the radius of the atom, which is about 70 picometers for Carbon-12. This calculation highlights the vast difference in scale between the atomic and nuclear volumes, illustrating the relative size of the nucleus compared to the entire atom.
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02:00Calculating Atomic Mass
Unit Conversion
Understanding unit conversion is crucial when calculating volumes in different units. In this case, converting femtometers to picometers (1 fm = 0.001 pm) is necessary to ensure consistency in measurements when calculating the volumes of the nucleus and the atom, allowing for accurate comparisons and results.
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01:56Conversion Factors
Related Practice
Textbook Question
Nuclei with the same number of neutrons but different mass numbers are called isotones. Write the symbols of four isotones of 236Th.
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Textbook Question
Neutron stars are composed of solid nuclear matter, primarily neutrons. Assume the radius of a neutron is approximately 1.0×10–13 cm. Calculate the density of a neutron. [Hint: For a sphere V = (4/3)πr3.] Assuming that a neutron star has the same density as a neutron, calculate the mass (in kg) of a small piece of a neutron star the size of a spherical pebble with a radius of 0.10 mm.
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Textbook Question
Carbon-12 contains six protons and six neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers). What percentage of the carbon atom's volume is occupied by the nucleus? (Assume two significant figures.)
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Textbook Question
A penny has a thickness of approximately 1.0 mm. If you stacked Avogadro's number of pennies one on top of the other on Earth's surface, how far would the stack extend (in km)? [For comparison, the sun is about 150 million km from Earth and the nearest star (Proxima Centauri) is about 40 trillion km from Earth.]
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Textbook Question
Consider the stack of pennies in the previous problem. How much money (in dollars) would this represent? If this money were equally distributed among the world's population of 7.0 billion people, how much would each person receive? Would each person be a millionaire? A billionaire? A trillionaire?
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