题目内容
如图所示,在某一足够大的真空室中,虚线PH的右侧是一磁感应强度为B、方向垂直纸面向里的匀强磁场,左侧是一场强为E、方向水平向左的匀强电场.在虚线PH上的点O处有一质量为M、电荷量为Q的镭核(
Ra).某时刻原来静止的镭核水平向右放出一个质量为m、电荷量为q的
粒子而衰变为氡(Rn)核,设
粒子与氡核分离后它们之间的作用力忽略不计,涉及动量问题时,亏损的质量可不计.
(1)写出镭核衰变为氡核的核反应方程;
(2)经过一段时间
粒子刚好到达虚线PH上的A点,测得
= L.求此时刻氡核的速率。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146384514405.jpg)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638357245.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638373219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638373219.gif)
(1)写出镭核衰变为氡核的核反应方程;
(2)经过一段时间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638373219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638420249.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241146384514405.jpg)
(1) 核反应方程为.![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638467446.gif)
(2)此时刻氡核的速率![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638482655.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638467446.gif)
(2)此时刻氡核的速率
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638482655.gif)
:(1) 核反应方程为.![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638467446.gif)
(2)设衰变后,氡核的速度为
,
粒子速度为
,由动量守恒定律得
,
粒子在匀强磁场中做匀速圆周运动,到达A点需要的时间为
,又![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638607408.gif)
氡核在电场中做匀加速直线运动,t时刻速度为v=
+at,
氡核的加速度为
,
由以上各式解得![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638482655.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638467446.gif)
(2)设衰变后,氡核的速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638513225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638373219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638545225.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638560379.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638373219.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638591316.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638607408.gif)
氡核在电场中做匀加速直线运动,t时刻速度为v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638513225.gif)
氡核的加速度为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638638414.gif)
由以上各式解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824114638482655.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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