Chemistry Exam > Chemistry Questions > A quantum mechanical particle of mass ‘...
Start Learning for Free
A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?
Correct answer is '9'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A quantum mechanical particle of mass ‘m’ free to rotate o...
$m$ is described by a wave function $\Psi(x,t)$, where $x$ is the particle's position and $t$ is time. The wave function satisfies the Schrödinger equation:
$$i\hbar\frac{\partial \Psi}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi}{\partial x^2}+V(x)\Psi$$
where $\hbar$ is the reduced Planck constant and $V(x)$ is the potential energy function.
The wave function contains all the information about the particle's position, momentum, and energy. The probability of finding the particle in a particular location $x$ is given by $|\Psi(x,t)|^2$. The expectation value of the position and momentum of the particle are given by:
$$\langle x \rangle =\int_{-\infty}^{\infty}x|\Psi(x,t)|^2dx$$
and
$$\langle p \rangle =\int_{-\infty}^{\infty}\Psi^*(x,t)\frac{\hbar}{i}\frac{\partial \Psi(x,t)}{\partial x}dx$$
respectively.
The wave function evolves in time according to the Schrödinger equation. This means that the probability distribution and expectation values of position and momentum change with time. The behavior of the wave function is subject to certain boundary conditions, such as being continuous and finite, and to the nature of the potential energy function.
$$i\hbar\frac{\partial \Psi}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi}{\partial x^2}+V(x)\Psi$$
where $\hbar$ is the reduced Planck constant and $V(x)$ is the potential energy function.
The wave function contains all the information about the particle's position, momentum, and energy. The probability of finding the particle in a particular location $x$ is given by $|\Psi(x,t)|^2$. The expectation value of the position and momentum of the particle are given by:
$$\langle x \rangle =\int_{-\infty}^{\infty}x|\Psi(x,t)|^2dx$$
and
$$\langle p \rangle =\int_{-\infty}^{\infty}\Psi^*(x,t)\frac{\hbar}{i}\frac{\partial \Psi(x,t)}{\partial x}dx$$
respectively.
The wave function evolves in time according to the Schrödinger equation. This means that the probability distribution and expectation values of position and momentum change with time. The behavior of the wave function is subject to certain boundary conditions, such as being continuous and finite, and to the nature of the potential energy function.
|
Explore Courses for Chemistry exam
|
|
Similar Chemistry Doubts
A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer?
Question Description
A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer?.
A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer?.
Solutions for A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? in English & in Hindi are available as part of our courses for Chemistry.
Download more important topics, notes, lectures and mock test series for Chemistry Exam by signing up for free.
Here you can find the meaning of A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer?, a detailed solution for A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? has been provided alongside types of A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A quantum mechanical particle of mass ‘m’ free to rotate on a surface of sphere of radius ‘r’ is in the state with energy 10h2/mr2. The degeneracy of the state is?Correct answer is '9'. Can you explain this answer? tests, examples and also practice Chemistry tests.
|
|
Explore Courses for Chemistry exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup