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Since it is bound, the mass of the deuteron is less than the sum of the masses of the neutron and the proton which make it up: (m, + mp) – ma = € = 2.22 MeV/c². Now, a photon with energy of 2.22 MeV has enough energy to break apart a deuteron into a neutron and a proton, both at rest. However, that process will not conserve momentum. A photon that could actually dissociate the deuteron (necessarily conserving both momentum and energy in the process) must have somewhat higher energy than 2.22 MeV. Your goal is to estimate how much. In the end you would like to say that the minimum energy of the required photon is Ey = 2.22 MeV(1 + a), and be able to say what the factor a actually is. There is a slight complication to this calculation which you should ignore for simplicity. The mass of the neutron (939.5 MeV/c²) and that of the proton (938.3 MeV/c²) are not identical. But, for the purposes of this calculation, go ahead and assume that they are the same; That is, assume that the deuteron splits into two exactly equal mass particles (mass m such that 2m – ma = €). Once you have an expression for the factor a you can put in the values e = 2.22 MeV/c² and ma = 1.88 GeV/c². [Hint: Be sure you understand the argument we have discussed for establishing the threshold energy for et - e- pair production.]

Since it is bound, the mass of the deuteron is less than the sum of the masses of the neutron and the proton which make it up: (m, + mp) – ma = € = 2.22 MeV/c². Now, a photon with energy of 2.22 MeV has enough energy to break apart a deuteron into a neutron and a proton, both at rest. However, that process will not conserve momentum. A photon that could actually dissociate the deuteron (necessarily conserving both momentum and energy in the process) must have somewhat higher energy than 2.22 MeV. Your goal is to estimate how much. In the end you would like to say that the minimum energy of the required photon is Ey = 2.22 MeV(1 + a), and be able to say what the factor a actually is. There is a slight complication to this calculation which you should ignore for simplicity. The mass of the neutron (939.5 MeV/c²) and that of the proton (938.3 MeV/c²) are not identical. But, for the purposes of this calculation, go ahead and assume that they are the same; That is, assume that the deuteron splits into two exactly equal mass particles (mass m such that 2m – ma = €). Once you have an expression for the factor a you can put in the values e = 2.22 MeV/c² and ma = 1.88 GeV/c². [Hint: Be sure you understand the argument we have discussed for establishing the threshold energy for et - e- pair production.]

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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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The deuteron is a bound state of a neutron and a proton. Suppose we wanted to break the deuteron apart into its constituent particles by hitting it with a photon (a process known as photodissociation). That is, letting y,d,n, and p represent the photon, deuteron, neutron, and proton, respectively, y +d → n + p + energy.
Transcribed Image Text:The deuteron is a bound state of a neutron and a proton. Suppose we wanted to break the deuteron apart into its constituent particles by hitting it with a photon (a process known as photodissociation). That is, letting y,d,n, and p represent the photon, deuteron, neutron, and proton, respectively, y +d → n + p + energy.
Since it is bound, the mass of the deuteron is less than the sum of the masses of the neutron and the proton which make it up: (m, + m,) – ma = e = 2.22 MeV/c?. Now, a photon with energy of 2.22 MeV has enough energy to break apart a deuteron into a neutron and a proton, both at rest. However, that process will not conserve momentum. A photon that could actually dissociate the deuteron (necessarily conserving both momentum and energy in the process) must have somewhat higher energy than 2.22 MeV. Your goal is to estimate how much. In the end you would like to say that the minimum energy of the required photon is Ey = 2.22 MeV(1 + a), and be able to say what the factor a actually is. There is a slight complication to this calculation which you should ignore for simplicity. The mass of the neutron (939.5 MeV/c2) and that of the proton (938.3 MeV/c2) are not identical. But, for the purposes of this calculation, go ahead and assume that they are the same; That is, assume that the deuteron splits into two exactly equal mass particles (mass m such that 2m – ma = e). Once you have an expression for the factor a you can put in the values e = 2.22 MeV/c? and mą = 1.88 GeV/c²?. [Hint: Be sure you understand the argument we have discussed for establishing the threshold energy for et – e- pair production.]
Transcribed Image Text:Since it is bound, the mass of the deuteron is less than the sum of the masses of the neutron and the proton which make it up: (m, + m,) – ma = e = 2.22 MeV/c?. Now, a photon with energy of 2.22 MeV has enough energy to break apart a deuteron into a neutron and a proton, both at rest. However, that process will not conserve momentum. A photon that could actually dissociate the deuteron (necessarily conserving both momentum and energy in the process) must have somewhat higher energy than 2.22 MeV. Your goal is to estimate how much. In the end you would like to say that the minimum energy of the required photon is Ey = 2.22 MeV(1 + a), and be able to say what the factor a actually is. There is a slight complication to this calculation which you should ignore for simplicity. The mass of the neutron (939.5 MeV/c2) and that of the proton (938.3 MeV/c2) are not identical. But, for the purposes of this calculation, go ahead and assume that they are the same; That is, assume that the deuteron splits into two exactly equal mass particles (mass m such that 2m – ma = e). Once you have an expression for the factor a you can put in the values e = 2.22 MeV/c? and mą = 1.88 GeV/c²?. [Hint: Be sure you understand the argument we have discussed for establishing the threshold energy for et – e- pair production.]
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