Question

Show that $R_{2,0}(r) = \frac{1}{\sqrt{8}} \left(\frac{1}{a_0}\right)^{\frac{3}{2}} \left(2 - \frac{r}{a_0}\right) e^{-\frac{r}{2a_0}}$ satisfies the Radial Schrodinger equation with eigenvalue $E_2 = -\frac{me^4}{32h^2}$.

Name: Show that R2,0(r) = (1)/(√(8))((1)/(a0))^(3)/(2)(2 - (r)/(a0)) e^-(r)/(2a0) satisfies the Radial Schrodinger equation with eigenvalue E2 = -(me^4)/(32h^2).
Uploaded: 2023-01-22T05:30:59-08:00
Duration: 1 min 56 s
Channel: Sri K
Description: Show that R2,0(r) = (1)/(√(8))((1)/(a0))^(3)/(2)(2 - (r)/(a0)) e^-(r)/(2a0) satisfies the Radial Schrodinger equation with eigenvalue E2 = -(me^4)/(32h^2).

          Show that $R_{2,0}(r) = \frac{1}{\sqrt{8}} \left(\frac{1}{a_0}\right)^{\frac{3}{2}} \left(2 - \frac{r}{a_0}\right) e^{-\frac{r}{2a_0}}$ satisfies the Radial Schrodinger equation with eigenvalue $E_2 = -\frac{me^4}{32h^2}$.

Added by Brad W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

01/22/2023

Step 1

Step 1: Start with the radial Schrodinger equation for hydrogen atom: \[ \left( -\frac{\hbar^2}{2\mu} \frac{d^2}{dr^2} + \frac{\hbar^2}{2\mu} \frac{l(l+1)}{r^2} - \frac{e^2}{4\pi\epsilon_0 r} - E \right) R_{nl}(r) = 0 \] where $ \mu $ is the reduced mass, $ l $ Show more…

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Show that R_(2,0)(r) = (1) / (sqrt{8}) ((1) / (a_(0)))^((3) / (2)) (2 - (r) / (a_(0))) e^(- (r) / (2a_(0))) satisfies the Radial Schrodinger equation with eigenvalue E_(2) = - (m_(e)e^(4)) / (32h^(2)). Show that R2.o(r) = 2a0 satisfies the Radial Schrodinger equation with eigenvalue E2 = mee4 32h2