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Lesson 8.1.1, lesson 8.1.2, lesson 8.1.3, lesson 8.1.4, lesson 8.1.5, lesson 8.2.1, lesson 8.2.2, lesson 8.3.1, lesson 8.3.2, lesson 8.3.3.
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58. The wave function for the 1 s state of an electron in the hydrogen atom is ψ1 s(ρ)=1/√(πa03) e-ρ/ a0where a0 is the Bohr radius. The probability of finding the electron in a region W of R3 is equal to ∭W p(x, y, z) d Vwhere, in spherical coordinates, p(ρ)=|ψ1 s(ρ)|2Use integration in spherical coordinates to show that the probability of finding the electron at a distance greater than the Bohr radius is equal to 5 / e2 ≈0.677. (The Bohr radius is a0=5.3 ×10-11 m, but this value is not needed.)
Define the probability density function as:
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- The wave function for the state of an electron in the hydrogen atom is where is the Bohr radius. The probability of finding the electron in a region of is equal to where, in spherical coordinates, Use integration in spherical coordinates to show that the probability of finding the electron at a distance greater than the Bohr radius is equal to . (The Bohr radius is , but this value is not needed.)
- The wave function for the orbital in the hydrogen atom is where is the value for the radius of the first Bohr orbit in meters is is the value for the distance from the nucleus in meters, and is an angle. Calculate the value of at for ( axis and for ( plane).
- The wave function for the orbital in the hydrogen atom is where is the value for the radius of the first Bohr orbit in meters is is the value for the distance from the nucleus in meters, and is an angle. Calculate the value of at for axis) and for ( plane).
- The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (a) What is the probability of finding the electron inside a sphere of volume , centered at the nucleus ? (b) (b) What is the probability of finding the electron in a volume of at a distance of from the nucleus, in a fixed but arbitrary direction?
(c) What is the probability of finding the electron in a spherical shell of in thickness, at a distance of from the nucleus?
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Lesson 8.1.3 b: A = 600 sq. cm, P z 108.3 cm QR (Reflexive Property), so APQR ASRQ (SSS z) 10 = 360. The other two angles must be equal since
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The wave function for the 1 s state of an electron in the hydrogen atom is ψ1 s (ρ)=1/√ (πa03) e-ρ/ a0where a0 is the Bohr radius. The probability of finding the electron in a region W of R3 is equal to ∭W p (x, y, z) d Vwhere, in spherical coordinates, p (ρ)=|ψ1 s (ρ)|2Use integration in spherical coordinates to show that the ...