Question

the wave function,ψ_1s, for the 1s electron in a hydrogen atom, is given by, where ψ_100find the most probablevalue of the radius, r, for this 1s electron.

Answer 1

The most probable value of the radius for the 1s electron in a hydrogen atom is 0.529 Å (52.9 pm). This radius is derived using the radial probability density function and corresponds to the prediction of Bohr's model.

Step-by-step explanation:

The most probable value of the radius for the 1s electron in a hydrogen atom can be determined using the radial probability density function. The probability density function, P(r), represents the probability of finding the electron in a given radial range. To find the most probable radial position, we set the first derivative of P(r) to zero and solve for r.

In the ground state of the hydrogen atom, the peak in the radial probability plot occurs at r = 0.529 Å (52.9 pm), which is the most probable radius for the 1s electron.

This most probable radius corresponds to the radius predicted by Bohr's model of the hydrogen atom.