H-atom. The wave function of one of the electrons in the 2p orbital is given by (ignoring spin) r 2,1,0 (1,0,0)= - 7 exp(-270) c ao 1 |32πα cose Where do is the Bohr radius. In the Bohr model, the radius of the electron orbit is given by m=2 = n²ao = 4ao. The probability that the electron can be found at some radius between r and r + dr is given by 2π P(r) dr = √2 = √ ₁²³ do 5° ² sin 0 de | Yn.l.m² (r, $,0)|²r² dr What is the expectation value of the distance of the electron from the nucleus (r)? Clue: expected value is computed by (r) = frP(r) dr then do integration by parts

H-atom. The wave function of one of the electrons in the 2p orbital is given by (ignoring spin) r 2,1,0 (1,0,0)= - 7 exp(-270) c ao 1 |32πα cose Where do is the Bohr radius. In the Bohr model, the radius of the electron orbit is given by m=2 = n²ao = 4ao. The probability that the electron can be found at some radius between r and r + dr is given by 2π P(r) dr = √2 = √ ₁²³ do 5° ² sin 0 de | Yn.l.m² (r, $,0)|²r² dr What is the expectation value of the distance of the electron from the nucleus (r)? Clue: expected value is computed by (r) = frP(r) dr then do integration by parts