题目

Aproton(mass1.6726×10−27kg)andaneutron(mass1.6749×10−27kg)at rest interact to form a deuterium nucleus (heavy hydrogen).In this process,a gamma ray (high energy photon) is emitted.The energy of this gamma ray is measured to be
2.2MeV≡2.2×106 eV.
a) What is the mass of the deuteron?Assume that you can neglect the small kinetic energy of the deuteron acquires after emitting the gamma ray,but keep all five significant figures as you calculate.
b) If we include the emitted gamma ray along with the proton and neutron (now bound in the deuteron) in the final state of the system to which we apply the momentum principle,we conclude that the system’s momentum must be conserved.That is,the deuteron must recoil with momentum equal and opposite to the momentum of the emitted gamma ray.Estimate the kinetic energy of the recoiling deuteron and verify that it is indeed small compared to the energy of the gamma ray,as assumed in part a).

提问时间：2021-01-03

答案

e=mc^2,也就是说在忽略重核动能的假设下,系统损失质量为3.91643*10^-30kg最后的重量为3.34358*10^-27kg.
下面是第二问,光子是微观物质,所以不能用经典力学解释,就用普朗克的公式.e=hν=hc/λ=pc.,p=1.17493*10^-21.我们在研究重核是则采用经典力学的方法.因为是估算吗.最后解出动能是4.12868*10^-16.而光子的能量是3.52479*10^-13,相差三个数量级,符合足够小的估算标准.
下面是具体演算过程
In[1]:= 2.2*10^6*1.60217653*10^-19
Out[1]= 3.52479*10^-13
In[3]:= 3.5247883659999994*10^-13/(9*10^16)
Out[3]= 3.91643*10^-30
In[4]:= 1.6726*10^-27 + 1.6749*10^-27 - 3.916431517777777*10^-30
Out[4]= 3.34358*10^-27
In[5]:= 3.5247883659999994`*^-13/(3*10^8)
Out[5]= 1.17493*10^-21
In[6]:= 1.1749294553333331`*^-21/3.3435835684822224`*^-27
Out[6]= 351398.
In[7]:= 351398^2*3.3435835684822224`*^-27
Out[7]= 4.12868*10^-16
以上单位都是国际标准单位.注意单位换算.