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For an electron in a hydrogen atom, the wave function, ψ is proportional to exp(-r/a0), where a0 is the Bohr’s radius. What is the ratio of the probability of finding the electron at the nucleus to the probability of finding it at a0:
- a)e
- b)e2
- c)1/e2
- d)Zero
Correct answer is option 'D'. Can you explain this answer?
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For an electron in a hydrogen atom, the wave function, ψ is propor...
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For an electron in a hydrogen atom, the wave function, ψ is propor...
In quantum mechanics, the wave function of an electron in a hydrogen atom is given by the Schrödinger equation:
Ψ(r,θ,φ) = R(r)Y(θ,φ)
where Ψ is the wave function, r is the radial distance from the nucleus, θ is the polar angle, and φ is the azimuthal angle. R(r) is the radial part of the wave function, which depends only on the radial distance r, and Y(θ,φ) is the angular part of the wave function, which depends only on the angles θ and φ.
The radial part of the wave function is given by:
R(r) = (1/n)^(3/2) * (2/nr)^3/2 * e^(-r/nr)
where n is the principal quantum number and nr is the Bohr radius.
The angular part of the wave function is given by:
Y(θ,φ) = θ(θ) * φ(φ)
where θ(θ) is the polar angle dependence and φ(φ) is the azimuthal angle dependence. The specific forms of these functions depend on the quantum numbers of the electron, such as the orbital angular momentum quantum number (l) and the magnetic quantum number (m).
Ψ(r,θ,φ) = R(r)Y(θ,φ)
where Ψ is the wave function, r is the radial distance from the nucleus, θ is the polar angle, and φ is the azimuthal angle. R(r) is the radial part of the wave function, which depends only on the radial distance r, and Y(θ,φ) is the angular part of the wave function, which depends only on the angles θ and φ.
The radial part of the wave function is given by:
R(r) = (1/n)^(3/2) * (2/nr)^3/2 * e^(-r/nr)
where n is the principal quantum number and nr is the Bohr radius.
The angular part of the wave function is given by:
Y(θ,φ) = θ(θ) * φ(φ)
where θ(θ) is the polar angle dependence and φ(φ) is the azimuthal angle dependence. The specific forms of these functions depend on the quantum numbers of the electron, such as the orbital angular momentum quantum number (l) and the magnetic quantum number (m).
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For an electron in a hydrogen atom, the wave function, ψ is proportional to exp(-r/a0), where a0 is the Bohr’s radius. What is the ratio of the probability of finding the electron at the nucleus to the probability of finding it at a0:a)eb)e2c)1/e2d)ZeroCorrect answer is option 'D'. Can you explain this answer?
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