Question

(1 point) Find the position of the first radial node in the 2s orbitals of atomic hydrogen, He+, and Li2+. Briefly explain the origin of the trend in these values.

Answer 1

The wave function that describes an electron in an atom is actually a product between the radial wave function, which is of interest in your case, and the angular wave function.

The radial wave function depends only on the distance from the nucleus, r.

Now, a node occurs when a wave function changes signs, i.e. when its passes through zero. A radial node occurs when a radial wave function passes through zero.

The important thing to remember about nodes is that an electron has zero probability of being located at a node. The probability of an electron being located at a particular point is given by the square of the absolute value of the wave function, |Ψ(x)|^2.

Since you have zero probability of locating an electron at a node, you can say that you have

|Ψ(x)|^2=0

Radical wave length fer 2s orbital Ractr)2) - e 240 Yis) = Ys R2s Cr) Yas)- angular cor ponal Yeas 24(2- ) e0 19012 2- for Nedes ts 2-0 l(2- 2r 290 3 C10 (a-2 2=290

atomic number ao atomie adi'us ot hydgen di'stamce brom muales గ for hydmgen atomiemumber z-1 290 290 ter Het chelum) atemic mumber 7-2 290 1 2+ for it (Lithium) atomic number z-3 290