Skip to main content
Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Brown 14th EditionCh.6 - Electronic Structure of Atoms문제 98
6장, 문제 98

Consider the discussion of radial probability functions in 'A Closer Look' in Section 6.6. (a) What is the difference between the probability density as a function of r and the radial probability function as a function of r ?

검증된 단계별 안내
1
The probability density function, often denoted as \( \psi^2 \), represents the probability per unit volume of finding an electron at a distance \( r \) from the nucleus.
The radial probability function, on the other hand, is the probability of finding an electron within a spherical shell at a distance \( r \) from the nucleus.
The radial probability function is obtained by multiplying the probability density by the surface area of the spherical shell, which is \( 4\pi r^2 \).
Thus, the radial probability function is given by \( 4\pi r^2 \psi^2 \), which accounts for the volume element in spherical coordinates.
In summary, while the probability density gives a local probability per unit volume, the radial probability function provides the total probability at a given radius, considering the entire spherical shell.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Probability Density

Probability density refers to the likelihood of finding an electron in a specific region of space at a given distance from the nucleus. It is represented as a function of the radial distance 'r' and is calculated from the square of the wave function. This concept is crucial for understanding how electron distribution varies in an atom.
추천 영상:
가이드 코스
01:56
Density Concepts

Radial Probability Function

The radial probability function describes the probability of finding an electron within a thin spherical shell at a distance 'r' from the nucleus. It is derived from the probability density and incorporates the volume of the spherical shell, which increases with 'r'. This function provides a more comprehensive view of electron distribution in three-dimensional space.
추천 영상:
가이드 코스
03:37
Logarithmic Functions

Spherical Coordinates

Spherical coordinates are a system of coordinates that define a point in three-dimensional space using three values: the radial distance from the origin, the polar angle, and the azimuthal angle. This system is particularly useful in quantum mechanics for describing the behavior of electrons in atoms, as it aligns with the symmetry of atomic orbitals.
추천 영상:
가이드 코스
00:27
Coordination Numbers
관련 실천
교과서 질문

As discussed in the A Closer Look box on 'Measurement and the Uncertainty Principle,' the essence of the uncertainty principle is that we can't make a measurement without disturbing the system that we are measuring. (a) Why can't we measure the position of a subatomic particle without disturbing it?

479
views
교과서 질문

The Chemistry and Life box in Section 6.7 described the techniques called NMR and MRI. (a) Instruments for obtaining MRI data are typically labeled with a frequency, such as 600 MHz. In what region of the electromagnetic spectrum does a photon with this frequency belong?

교과서 질문

The Chemistry and Life box in Section 6.7 described the techniques called NMR and MRI. (c) When the 450-MHz photon is absorbed, does it change the spin of the electron or the proton on a hydrogen atom?

401
views