The size of one-electron atoms

If the expression the size of an atom is to have any meaning, it must have something to do with the distance between the electron and the nucleus. Several definitions are possible at this stage we choose to identify the atomic radius with the maximum distance allowed by classical physics, equation (1.7)  

The information in equations (1.13) and (1.14) may be summarized as follows As the principal quantum number n increases, the radius of the atom increases by n, and the ionization energy decreases by the factor /n.  

Comparing one-electron atoms with the same value for the principal quantum number, we see that when the nuclear charge Z increases, the size of the atom decreases by a factor ofl/Z while the ionization energy increases by a factor ofZ.  

Problem 1.4 What is the radius (rmax) of a hydrogen atom in the ground state What is the size of a H atom with principal quantum number n = 10 000 The circumference of the Earth is 40 000 km. What would be the principal quantum number of a hydrogen atom with the same size (It would obviously be difficult to find a container for such an atom ) 

Problem 1.5 Calculate the ratio between the volumes and between the mass densities of H and He atoms in the ground state. 

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