Consider the discussion of radial probability functions in 'A Closer Look' in Section 6.6. (a) What is the difference between the probability density as a function of r and the radial probability function as a function of r ?

Video transcript

Hey everyone in this example, we need to express probability density and radial probability function as functions of radius. So we should first recall that probability density is expressed bye. Our wave function, which is represented by this symbol multiplied by our radius squared. And actually we should have brackets so that we calculate this portion first and then we square our answer. We should recall that probability density describes the probability of finding an electron at a single point at the distance R from the nucleus. So for our radial probability function, we're going to interpret that here below. We should recall that that's calculated by taking four times our wave function multiplied by R squared. And this describes the probability of finding an electron at any point on the sphere defined by radius. So integrating these two formulas together, we can conclude that the probability of our radius is equal to four times our wave function multiplied by the radius squared, which is then multiplied by the brackets. Where we have our probability density, which again is our wave function multiplied by the radius and then squared outside of the brackets. So this would be our final answer. Where we interpret the probability density and radial probability function as functions of radius. If you have any questions, please leave them down below. Otherwise, I'll see everyone in the next practice video