Analyze the radial distribution of the H-atom at the 2s state. How are the maxima
situated with respect to the minimum?
To analyze the radial distribution of the H-atom at the 2s state, we need to understand the concept of radial probability distribution.
The radial probability distribution describes the probability of finding an electron in a particular volume element at a given distance from the nucleus. The probability is given by the square of the wave function, which depends on the principal quantum number (n) and the azimuthal quantum number (l).
For the 2s state of the hydrogen atom, the principal quantum number (n) is 2 and the azimuthal quantum number (l) is 0. The radial probability distribution for a 2s orbital is given by:
P(r) = (4 / (a^3) * exp(-2r/a) * (r^2)),
where 'r' is the distance from the nucleus, 'a' is the Bohr radius (0.529 Å), and 'exp' denotes the exponential function.
To analyze the radial distribution, we need to plot the radial probability distribution as a function of distance (r) from the nucleus. We can choose a suitable range of 'r', such as from 0 to a maximum value.
The maxima of the radial distribution correspond to regions of higher electron density, while the minima correspond to regions of lower electron density. In the case of the 2s state, there is a single maximum at the nucleus (r = 0) and another maximum at a distance of approximately 1.27a.
The maximum at the nucleus represents the electron being closest to the nucleus, while the maximum at 1.27a represents the electron being at a distance where the probability of finding the electron is relatively high.
The minimum in the radial distribution occurs between the two maxima. This minimum represents a region of lower electron density, where the probability of finding the electron is relatively low.
In summary, for the radial distribution of the H-atom at the 2s state, there are two maxima situated at the nucleus and at a distance of approximately 1.27 times the Bohr radius, with a minimum in between.