Question

A diatomic molecule having atoms of masses $m_{1}$ and $m_{2}$ has its potential energy function about the equilibrium position $r_{0}$ as given by $U(r)=-A+B\left(r-r_{0}\right)^{2}$, where $A$ and $B$ are constants. When the atom vibrate at high temperature condition, the square of angular frequency of vibration will be (A) $\frac{2 B}{m_{1}}$ (B) $\frac{2 B}{m_{2}}$ (C) $\frac{2 B\left(m_{1}+m_{2}\right)}{m_{1} m_{2}}$ (D) $\frac{B\left(m_{1}+m_{2}\right)}{2 m_{1} m_{2}}$

Name: Problem 8, Chapter 11: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-09-25T17:11:49-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: A diatomic molecule having atoms of masses m1 and m2 has its potential energy function about the equilibrium position r0 as given by U(r)=-A+B(r-r0)^2, where A and B are constants. When the atom vibrate at high temperature condition, the square of angular frequency of vibration will be (A) (2 B)/(m1) (B) (2 B)/(m2) (C) (2 B(m1+m2))/(m1 m2) (D) (B(m1+m2))/(2 m1 m2)

   A diatomic molecule having atoms of masses $m_{1}$ and $m_{2}$ has its potential energy function about the equilibrium position $r_{0}$ as given by $U(r)=-A+B\left(r-r_{0}\right)^{2}$, where $A$ and $B$ are constants. When the atom vibrate at high temperature condition, the square of angular frequency of vibration will be
(A) $\frac{2 B}{m_{1}}$
(B) $\frac{2 B}{m_{2}}$
(C) $\frac{2 B\left(m_{1}+m_{2}\right)}{m_{1} m_{2}}$
(D) $\frac{B\left(m_{1}+m_{2}\right)}{2 m_{1} m_{2}}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 11, Problem 8

Instant Answer

Solved by Expert Narayan Hari

09/25/2021

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This gives us $F=-\frac{dU}{dr}$. Show more…

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A diatomic molecule having atoms of masses $m_{1}$ and $m_{2}$ has its potential energy function about the equilibrium position $r_{0}$ as given by $U(r)=-A+B\left(r-r_{0}\right)^{2}$, where $A$ and $B$ are constants. When the atom vibrate at high temperature condition, the square of angular frequency of vibration will be (A) $\frac{2 B}{m_{1}}$ (B) $\frac{2 B}{m_{2}}$ (C) $\frac{2 B\left(m_{1}+m_{2}\right)}{m_{1} m_{2}}$ (D) $\frac{B\left(m_{1}+m_{2}\right)}{2 m_{1} m_{2}}$

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Key Concepts

Harmonic Oscillator Approximation

In molecular physics, the vibrational motion of a diatomic molecule near its equilibrium position can be modeled as a harmonic oscillator. This approximation involves expanding the potential energy curve around the equilibrium to a quadratic form, where the second derivative of the potential gives an effective force constant. The oscillator's angular frequency is then determined by this force constant divided by the mass term relevant to the system.

Reduced Mass

The reduced mass is a key concept in the dynamics of two-body systems, particularly in diatomic molecules. It is defined as ? = (m1*m2)/(m1+m2) and allows the two-body problem to be simplified into an equivalent one-body problem. In the context of molecular vibrations, the reduced mass is used in calculating the angular frequency of vibration as it effectively combines the masses of the two atoms.

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