Distribution function for 1s 2s and 3s 12E10 1E10 8E09 6E09

Distribution function for 1s, 2s, and 3s 1.2E+10 1E+10 8E+09 6E+09 4E+09 2E+09 1E-09 1.2E-09 4E-10 6E-10 8E-10 2E-10

Solution

(a) 1s has probability closest to nucleus. From the plot we can see the a peak of 1E+10 for 1s near to zero in X-axis. Here near to zero in X-axis means near to nucleus, so 1s has high probability at nucleus. Also, we can say 1s orbitals are the one which feels more nuclear charge and hence more attracted by nucleus and hence present near to nulceus.

(b) 3s has the largest average radius. Here, in the plot we can see abroad peak ranging in the X-axis from 4E-10 to 1.0E-09, where as for 1s and 2s it is quite nearer to zero. Hence if we average out the distance from nucleus, 3s will give a larger value. Also we can say, the 3s orbital feels less nuclear charge than 1s and 2s and hecne 3s will be more diffused and the average distance will be more.