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3. Calculate the probability to find an electron in the following regions if the electron resides in a 2p, orbital of a hydrogen atom. The "z" in the equation below is a Cartesian coordinate, not the atomic number "z" which equals 1 for the hydrogen atom. Use whatever information below is more convenient. 32 m až ao 1 3 Vzp, = R(r)Y(0, 4) where R(r) = 24 a ao and Y(0,4) = cos e (a) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (2a, 0, 0). (b) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 2as, 0). (c) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 0, 2a0).

3. Calculate the probability to find an electron in the following regions if the electron resides in a 2p, orbital of a hydrogen atom. The "z" in the equation below is a Cartesian coordinate, not the atomic number "z" which equals 1 for the hydrogen atom. Use whatever information below is more convenient. 32 m až ao 1 3 Vzp, = R(r)Y(0, 4) where R(r) = 24 a ao and Y(0,4) = cos e (a) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (2a, 0, 0). (b) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 2as, 0). (c) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 0, 2a0).

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3. Calculate the probability to find an electron in the following regions if the electron resides in a 2p: orbital of a hydrogen atom. The "z" in the equation below is a Cartesian coordinate, not the atomic number "2" which equals 1 for the hydrogen atom. Use whatever information below is more convenient. 32 n až ao 13 I and Y(0,4) =: 24 až ao Vzp, = R(r)Y(0, 4) where R(r) = (a) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (200, 0, 0). (b) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 2ao, 0). (c) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 0, 2a0). (d) Draw a 2p, orbital in 3D space and include the points of (a), (b), and (c). Explain how your diagram qualitatively supports the probabilities you calculated. (e) Calculate the probability to find an electron in a 1.0 pm-thick shell at a radius 2ao from the nucleus.
Transcribed Image Text:3. Calculate the probability to find an electron in the following regions if the electron resides in a 2p: orbital of a hydrogen atom. The "z" in the equation below is a Cartesian coordinate, not the atomic number "2" which equals 1 for the hydrogen atom. Use whatever information below is more convenient. 32 n až ao 13 I and Y(0,4) =: 24 až ao Vzp, = R(r)Y(0, 4) where R(r) = (a) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (200, 0, 0). (b) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 2ao, 0). (c) Calculate the probability to find an electron in a 1.0 pm' cube centered at the Cartesian point (0, 0, 2a0). (d) Draw a 2p, orbital in 3D space and include the points of (a), (b), and (c). Explain how your diagram qualitatively supports the probabilities you calculated. (e) Calculate the probability to find an electron in a 1.0 pm-thick shell at a radius 2ao from the nucleus.
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