题目内容
(附加题)(16分)钚的放射性同位素
静止时衰变为铀核激发态
和
粒子,而铀核激发态
立即衰变为铀核
,并放出能量为
的
光子。已知:
、
和
粒子的质量分别为
、
和
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137004391044.png)
(1)写出衰变方程;
(2)已知衰变放出的光子的动量可忽略,求
粒子的动能。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659191603.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659269647.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659300355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659269647.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659425608.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659440780.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659534355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659690657.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659425608.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659300355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659815990.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659893976.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659908850.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137004391044.png)
(1)写出衰变方程;
(2)已知衰变放出的光子的动量可忽略,求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659300355.png)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137004861133.png)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137011411017.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137004861133.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137011411017.png)
(1)衰变方程为
① (1分)
② (1分)
或合起来有
③
(2)上述衰变过程的质量亏损为
④ (2分)
放出的能量为
⑤ (2分)
这些核能是轴核
的动能
、
粒子的动能
和
光子的能量
之和
⑥ (1分)
由上式得
⑦ (1分)
设衰变后的轴核和
粒子的速度分别为
和
,则由动量守恒有
⑧ (2分)
又由动能的定义知
⑨ (2分)
由⑧⑨式得
⑩ (1分)
由⑦—⑩式得
(2分)
代入题给数据得
(1分)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137012031043.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137012342980.png)
或合起来有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137004861133.png)
(2)上述衰变过程的质量亏损为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701281910.png)
放出的能量为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701297796.png)
这些核能是轴核
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701328572.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701344474.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659300355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701406439.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659534355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701468464.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701484917.png)
由上式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137015781343.png)
设衰变后的轴核和
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113659300355.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701624505.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701640388.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701671751.png)
又由动能的定义知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137016871348.png)
由⑧⑨式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824113701718963.png)
由⑦—⑩式得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137017491797.png)
代入题给数据得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241137011411017.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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