2s ORBITAL 13 sented by a p jection of a sphere (a circle)surrounding the nucleus Erample.The numerical probability of finding the hydrogen electron within spheres of various radii from the nucleus is shown in Fig.1.3la.The circles represent con- tours of probability on a plane that bisects the sphere.If the contour circle of 0.95 probability is chosen.the electron is 19 times as likely to be inside the correspon- ding sphere with a radius of 1.7A as it is to be outside that sphere.The circle that is usually drawn, nt the is mply that t unspeci probabi of finding the electron in a sphere.of which the probability 0.95 0.9 07 0.5 0.3 0.4p11 20 radius(A) Figure 1.31.()The probability contours and radii for the hydrogen atom,the probability at the nucleus is zero.(b)Representation of the 1s orbital. 1.32 2s ORBITAL The spherically symmetrical orbital having one spherical nodal surface,that is.a sur face on which the probability of finding an electron is zero.Electrons in this orbital have the principal quantum number n=2,but have no angular momentum,that is, 1=0、m=0. Example.Figure 1.32 shows the probability distribution of the 2s electron as a cross the sphe ical 2s simple circlenodes. It is represented by a projection of a sphere (a circle) surrounding the nucleus, within which there is a specified probability of finding the electron. Example. The numerical probability of finding the hydrogen electron within spheres of various radii from the nucleus is shown in Fig. 1.31a. The circles represent con￾tours of probability on a plane that bisects the sphere. If the contour circle of 0.95 probability is chosen, the electron is 19 times as likely to be inside the correspon￾ding sphere with a radius of 1.7 Å as it is to be outside that sphere. The circle that is usually drawn, Fig. 1.31b, to represent the 1s orbital is meant to imply that there is a high, but unspecified, probability of finding the electron in a sphere, of which the circle is a cross-sectional cut or projection. 1.32 2s ORBITAL The spherically symmetrical orbital having one spherical nodal surface, that is, a sur￾face on which the probability of finding an electron is zero. Electrons in this orbital have the principal quantum number n
2, but have no angular momentum, that is, l
0, ml=0. Example. Figure 1.32 shows the probability distribution of the 2s electron as a cross section of the spherical 2s orbital. The 2s orbital is usually drawn as a simple circle of arbitrary diameter, and in the absence of a drawing for the 1s orbital for comparison, 2s ORBITAL 13 1.2 1.6 2.0 0.95 0.9 0.8 0.7 0.5 0.4 0.8 0.3 0.1 (a) (b) probability radius (Å) Figure 1.31. (a) The probability contours and radii for the hydrogen atom, the probability at the nucleus is zero. (b) Representation of the 1s orbital. c01.qxd 5/17/2005 5:12 PM Page 13