A diatomic molecule is made of two masses m_1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The rotational energy of a system is given by $E = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.According to

Vedclass · Accepted Answer

$\frac{(m_1 + m_2)n^2 h^2}{8 \pi^2 m_1 m_2 r^2}$

Vedclass · Answer

(A) The rotational energy of a system is given by $E = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.According to Bohr's quantization rule,$L = \frac{nh}{2\pi}$.The moment of inertia $I$ for a diatomic molecule about its center of mass is $I = \mu r^2$,where $\mu = \frac{m_1 m_2}{m_1 + m_2}$ is the reduced mass.Substituting $L$ and $I$ into the energy formula:$E = \frac{(nh/2\pi)^2}{2(\frac{m_1 m_2}{m_1 + m_2})r^2}$$E = \frac{n^2 h^2}{4\pi^2 \cdot 2 \cdot \frac{m_1 m_2}{m_1 + m_2} r^2}$$E = \frac{(m_1 + m_2)n^2 h^2}{8\pi^2 m_1 m_2 r^2}$.

$A$ diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization,its energy will be given by: ($n$ is an integer)

Similar Questions

What is the ratio of the area of the orbit of an electron in the first excited state to that in the ground state of a hydrogen atom (in $: 1$)?

The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$. What is the radius of the $n = 3$ orbit?

For an electron moving in the $n^{th}$ orbit of an $H$-atom,the angular velocity is proportional to:

The potential energy of a proton and an electron in a hydrogen atom is given by $V = V_0 \ln \left( \frac{r}{r_0} \right)$,where $r_0$ is a constant. Assuming the system follows the Bohr model,find the relationship between the radius $r_n$ and the principal quantum number $n$.

Neglecting the reduced mass effect,which optical transition in the $He^+$ spectrum has the same wavelength as the first Lyman transition of hydrogen ($n = 2$ to $n = 1$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module