Textbook Question
Each of the following transmutations produces a radionuclide used in positron emission tomography (PET).
(a) In equations (i) and (ii), identify the species signified as 'X.'
(i) 14N(p,α)X
(ii) 18O(p,X)18F
(iii) 14N(d,n)15O
Ch.21 - Nuclear Chemistry
Chapter 21, Problem 84
The Sun radiates energy into space at the rate of 3.9 * 1026 J/s. (a) Calculate the rate of mass loss from the Sun in kg/s. (b) How does this mass loss arise? (c) It is estimated that the Sun contains 9 * 1056 free protons. How many protons per second are consumed in nuclear reactions in the Sun?
Verified step by step guidance1
Step 1: To find the rate of mass loss from the Sun in kg/s, use Einstein's mass-energy equivalence principle, E=mc^2, where E is energy, m is mass, and c is the speed of light (approximately 3.00 x 10^8 m/s). Rearrange the formula to solve for mass: m = E/c^2.
Step 2: Substitute the given energy rate (3.9 x 10^26 J/s) into the equation from Step 1 to calculate the rate of mass loss. This will give you the mass loss in kg/s.
Step 3: For part (b), understand that the mass loss arises from nuclear fusion reactions occurring in the Sun's core, where hydrogen nuclei (protons) fuse to form helium, releasing energy in the process.
Step 4: To find how many protons per second are consumed, first determine the energy released per fusion reaction. Typically, the fusion of four protons into one helium nucleus releases about 26.7 MeV of energy.
Step 5: Convert the energy released per reaction from MeV to joules, then divide the total energy output of the Sun (3.9 x 10^26 J/s) by the energy per reaction to find the number of reactions per second. Since each reaction consumes four protons, multiply the number of reactions by four to find the number of protons consumed per second.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Einstein's Mass-Energy Equivalence
Einstein's mass-energy equivalence principle, expressed as E=mc², states that energy (E) and mass (m) are interchangeable; they are different forms of the same thing. This principle is crucial for understanding how the Sun converts mass into energy through nuclear fusion, allowing us to calculate the rate of mass loss based on the energy output.
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04:12
Energy to Mass Conversion
Nuclear Fusion in the Sun
Nuclear fusion is the process by which two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. In the Sun, hydrogen nuclei fuse to form helium, which is the primary source of the Sun's energy. This process not only generates energy but also results in a gradual loss of mass, which can be quantified.
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02:06Nuclear Binding Energy
Rate of Reaction and Particle Consumption
The rate of reaction in nuclear processes, such as those occurring in the Sun, can be determined by the energy produced and the number of particles involved. By knowing the total energy output and the energy released per fusion reaction, we can calculate how many protons are consumed per second, providing insight into the Sun's longevity and energy production.
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02:03Average Rate of Reaction