题目内容
氢原子基态能量E1=-13.6eV,电子绕核运动半径r1=0.53×10-10m.
求氢原子处于n=4激发态时:(电子的质量m=0.9×10-30kg)
(1)原子系统具有的能量;
(2)电子在轨道上运动的动能;
(3)电子具有的电势能;
(4)向低能级跃迁辐射的光子频率最多有多少种?其中最低频率为多少(保留两位有效数字)?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139031673.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139140548.png)
(1)原子系统具有的能量;
(2)电子在轨道上运动的动能;
(3)电子具有的电势能;
(4)向低能级跃迁辐射的光子频率最多有多少种?其中最低频率为多少(保留两位有效数字)?
(1)
(2)0.85eV(3)-1.7Ev(4)0.66eV
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139296958.png)
(1)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139296958.png)
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139499521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139592862.png)
所以动能![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241401396393073.png)
(3)由于![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139701648.png)
所以电势能![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139764874.png)
(4)最多有六种.从n=4→3;3→2;2→1;4→2;4→1;3→1.能级差最小的是n=4→n=3,所辐射的光子能量为:![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241401399041084.png)
本题考查的是对氢原子光谱能级及跃迁辐射的理解,根据玻尔氢原子理论和能级关系计算出氢原子处于n=4激发态时具有的能量;根据电子轨道特点计算出其动能;根据总能量等于势能加动能得到电势能;根据跃迁方式得到光子能量;
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139296958.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139499521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139592862.png)
所以动能
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241401396393073.png)
(3)由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139701648.png)
所以电势能
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140139764874.png)
(4)最多有六种.从n=4→3;3→2;2→1;4→2;4→1;3→1.能级差最小的是n=4→n=3,所辐射的光子能量为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241401399041084.png)
本题考查的是对氢原子光谱能级及跃迁辐射的理解,根据玻尔氢原子理论和能级关系计算出氢原子处于n=4激发态时具有的能量;根据电子轨道特点计算出其动能;根据总能量等于势能加动能得到电势能;根据跃迁方式得到光子能量;
![](http://thumb2018.1010pic.com/images/loading.gif)
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