Atomic StructureMedium
Question
A particle of mass $m$ is moving around the origin with a constant force $F$ pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the $n^{\text{th}\text{~}}$ orbit and the particle's speed $v$ in the orbit depend on $n$ as
Options
A.$r \propto n^{1/3};v \propto n^{1/3}$
B.$r \propto n^{1/3};v \propto n^{2/3}$
C.$r \propto n^{2/3};v \propto n^{1/3}$
D.$r \propto n^{4/3};v \propto n^{- 1/3}$
Solution
Given, force is constant
$$\begin{matrix} & & F = \frac{mv^{2}}{r} \\ & & \ \Rightarrow \frac{v^{2}}{r} = constant \\ & \ \Rightarrow r \propto v^{2}\ldots(1) & \text{(1)} \end{matrix}$$
$$\begin{array}{r} \text{~}\text{\&}\text{~}\ L = mvr = \frac{nh}{2\pi}\#(2) \end{array}$$
⇒ on solving equation (1) and equation (2)
$\nu \propto n^{1/3}$ and $r \propto n^{2/3}$
Create a free account to view solution
View Solution FreeMore Atomic Structure Questions
If the series limit frequency of the Lyman series is vL, then the series limit frequency of the Pfund series is :...The wave number of the series limit of lyman series is -...An α - particle of energy 5 MeV is scattered through 180o by a fixed uranium nucleus. The distance of the closest a...Which energy state of doubly ionized lithium (Li++) has the same energy as that of the ground state of hydrogen ? Given ...According to De Broglie, wavelength of electron in second orbit is 10-9 metre. Then the circumfrance of orbit is :-...