题目内容
质谱仪是一种分析同位素的重要工具,它的构造原理如图所示。离子源S产生质量为m、电荷量为q的钾离子,离子出来时速度很小,可视为零。离子经过电势差为U的电场加速后,沿着与磁场垂直的方向进入磁感应强度为B的匀强磁场,经半圆周到达照相底片上的P点。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032058683305.png)
(1)求粒子进入磁场时的速度
;
(2)求P点到入口S1的距离x;
(3)在实验过程中由于仪器不完善,加速电压在平均值U附近变化
U,求需要以多大相对精确度
U/U维持加速电压值,才能使钾39、钾41的同位素束在照相底片上不发生覆盖。
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032058683305.png)
(1)求粒子进入磁场时的速度
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205883323.png)
(2)求P点到入口S1的距离x;
(3)在实验过程中由于仪器不完善,加速电压在平均值U附近变化
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205899335.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205930319.png)
(1)
(2)
(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205993479.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205961721.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205977833.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205993479.png)
试题分析:(1)电场加速:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206024886.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205883323.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206055726.png)
(2)磁场偏转:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206071800.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206102738.png)
距离x
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032061171025.png)
(3)设钾39、钾41的质量分别为m1、m2,根据(2)问轨道半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206102738.png)
钾39在磁场中的最大半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032061641334.png)
钾41在磁场中的最小半径
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/201408250032061801327.png)
由题意知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206195656.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206227970.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003206242889.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140825/20140825003205993479.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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