The mass of Yukawa's meson can be estimated as follows. When two protons in a nucleus...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The mass of Yukawa's meson can be estimated as follows. When two protons in a nucleus exchange a meson (mass m.) they must wemporarily violate the conservation of energy by an amount me (the rest energy of the meson). The Heisenberg uncertainty principle says that you may "borrow" an energy AB, provided you "pay it back" in a time A given by APA = (where = /2x). In this case we need to borrow AB=m² long enough for the meson to make it from one proton to the other. It has to cross the nucleus (size), and it travels, presumably, at some substantial fraction of the speed of light, so, roughly speaking, At=/c. Putting this all together, we have 77₂ h roc Using To = 10-13 cm (the size of a typical nucleus), calculate the mass of Yukawa's meson. Express your answer as a multiple of the electron's mass, and compare the observed mass of the pion. [If you find that argument compelling, I can only say that you're pretty gullible. Try it for an atom, and you'll conclude that the mass of the photon is about 7 x 10-30g, which is nonsense. Nevertheless, it is a useful device for "back-of-the-envelope" calculations, and it does very well for the pi meson. Unfortunately, many books present it as though it were a rigorous derivation, which it certainly is not. The uncertainty principle does not license violation of conservation of energy (nor does any such violation occur in this process; we shall see later on how this comes about). Moreover, it's an inequality, ABAt >h, which at most could give you a lower bound on m. It is typically true that the range of a force is inversely proportional to the mass of the mediator, but the size of a bound state is not always a good measure of the range (that's why the argument fails for the photon: The range of the electromagnetic force is infinite, but the size of an atom is not). In general, when you hear a physicist invoke the uncertainty principle, keep a hand on your wallet.] The mass of Yukawa's meson can be estimated as follows. When two protons in a nucleus exchange a meson (mass m.) they must wemporarily violate the conservation of energy by an amount me (the rest energy of the meson). The Heisenberg uncertainty principle says that you may "borrow" an energy AB, provided you "pay it back" in a time A given by APA = (where = /2x). In this case we need to borrow AB=m² long enough for the meson to make it from one proton to the other. It has to cross the nucleus (size), and it travels, presumably, at some substantial fraction of the speed of light, so, roughly speaking, At=/c. Putting this all together, we have 77₂ h roc Using To = 10-13 cm (the size of a typical nucleus), calculate the mass of Yukawa's meson. Express your answer as a multiple of the electron's mass, and compare the observed mass of the pion. [If you find that argument compelling, I can only say that you're pretty gullible. Try it for an atom, and you'll conclude that the mass of the photon is about 7 x 10-30g, which is nonsense. Nevertheless, it is a useful device for "back-of-the-envelope" calculations, and it does very well for the pi meson. Unfortunately, many books present it as though it were a rigorous derivation, which it certainly is not. The uncertainty principle does not license violation of conservation of energy (nor does any such violation occur in this process; we shall see later on how this comes about). Moreover, it's an inequality, ABAt >h, which at most could give you a lower bound on m. It is typically true that the range of a force is inversely proportional to the mass of the mediator, but the size of a bound state is not always a good measure of the range (that's why the argument fails for the photon: The range of the electromagnetic force is infinite, but the size of an atom is not). In general, when you hear a physicist invoke the uncertainty principle, keep a hand on your wallet.]
Expert Answer:
Related Book For
University Physics with Modern Physics
ISBN: 978-0133977981
14th edition
Authors: Hugh D. Young, Roger A. Freedman
Posted Date:
Students also viewed these economics questions
-
What does Default Visibility Timeout refer to while configuring a queue in SQS?
-
The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
Consider an asset allocation problem with one risky asset and one risk-free asset .There are four investors .Each investor maximizes a mean-variance utility function to make their optimal investment...
-
You are thinking of making an investment in a new plant. The plant will generate revenues of $1 million per year for as long as you maintain it. You expect that the maintenance costs will start at...
-
In Problems 25-40, decide on a reasonable means for conducting the survey to obtain the desired information. The city council wants to use a survey to determine the extent of public approval for a...
-
In a second system of pulleys, there are 5 pulleys in each block. If an effort of 150 N can just lift a load of 1400 N, find (a) the effort wasted in friction, and (b) load wasted in friction.
-
During the recession of 19891993, the auto industry began taking extreme cost cutting measures by downsizing its organizations. The downsizing efforts created project management problems for the...
-
What is the angular diameter (in arcseconds) of a comet nucleus that has a radius of 15.0 km and is located at a distance of 3.00 Astronomical Units.
-
At December 31, 20X0, Oettinger Corporation, a premium kitchen cabinetmaker for the home remodeling industry, reported the following accounts receivable information on its year-end balance sheet:...
-
As an entrepreneur running a small business, do you think it is better to keep close control of cash or worry about how profitable you are? Why do you think one is more or less important than the...
-
-5 a) Calculate 2 = (-23+2i) and write the answer Cartesian form. on b) solve the equation 2+(4+2i)z+ (12-4) 0 +H
-
What is the output of the given code block? = 10 a b = 20 C = 30 if a % b > 1: print(a * b) elif b % a == 10: print (b a) print(c % 11) ww
-
19. Construct the flowchart and algorithm of the following problem: A fishing fleet fishes in 10 different regions each consisting of 8 different areas. The data about the fish caught in kilograms...
-
Given the graph of y = f(x) below, answer all of the following questions. -5 1 y 5 Activa
-
What are the definitions for these words? administrative law, cause of action, civil law, compensatory damages, constitutional law, contract, demurrer, depose, due diligence, felony, laws,...
-
Mike has $25,000 in his personal checking account, $50,000 in a joint checking account with his wife, and a $5,000 savings bond, all at an FDIC-insured institution. How much does Mike have insured...
-
A. Select a recent issue (paper or online) of Report on Business Magazine, Canadian Business Magazine (online only), Bloomberg Businessweek, Fast Company, The Economist, or another business magazine....
-
A very heavy SUV collides head-on with a very light compact car. Which of these statements about the collision are correct? (a) The amount of kinetic energy lost by the SUV is equal to the amount of...
-
A student claims that she can start a fire on a sunny day using just the suns rays and a concave mirror. How is this done? Is the concept of image relevant? Can she do the same thing with a convex...
-
A 0.250-m-long bar moves on parallel rails that are connected through a 6.00-Ω resistor, as shown in Fig. E29.33, so the apparatus makes a complete circuit. You can ignore the resistance...
-
What is the value of Brunei Petroleum Companys preferred stock when the dividend rate is 18 percent on a $100 par value? The appropriate discount rate for a stock of this risk level is 14 percent.
-
The preferred stock of the Luxemburg Mining Corporation pays a $3.25 dividend. What is the value of the stock if your required rate of return is 8 percent?
-
You are considering an investment in one of the preferred stocks of either Longines Watch Company or Titoni Watch Company. Longiness preferred stock pays an annual dividend of \($2.73,\) while that...
Study smarter with the SolutionInn App