Which of the following statements are true re | vedclass

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

Question

(A) According to Bohr's model for a hydrogen atom:$(I)$ The orbital speed $v_n$ is given by $v_n \propto \frac{1}{n}$. As $n$ increases (moving away f

Vedclass · Accepted Answer

$I$ and $III$

Vedclass · Answer

(A) According to Bohr's model for a hydrogen atom:$(I)$ The orbital speed $v_n$ is given by $v_n \propto \frac{1}{n}$. As $n$ increases (moving away from the nucleus),$v_n$ decreases. Thus,statement $(I)$ is true.$(II)$ The radius of the $n^{th}$ orbit is $r_n \propto n^2$. Statement $(II)$ is false because it is proportional to the square of the principal quantum number.$(III)$ The frequency of revolution $f$ is given by $f = \frac{v}{2\pi r}$. Since $v \propto \frac{1}{n}$ and $r \propto n^2$,we have $f \propto \frac{1/n}{n^2} = \frac{1}{n^3}$. Thus,statement $(III)$ is true.$(IV)$ The electrostatic binding force is $F = \frac{ke^2}{r^2}$. Since $r$ increases as $n$ increases,the force $F$ decreases. Thus,statement $(IV)$ is false.Therefore,statements $(I)$ and $(III)$ are correct.

Similar Questions

In a hydrogen atom in its ground state,the first Bohr orbit has radius $r_1$. The electron's orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is (in $r_1$)

The radius of the first orbit of a hydrogen atom is $0.5 \, \mathring{A}$ and the speed of the electron is $2.2 \times 10^6 \, m/s$. Find the magnetic induction at the proton due to the motion of the electron in $Tesla$.

The speed of an electron in the orbit of a hydrogen atom in the ground state is

The velocity of an electron in the second orbit of a sodium atom (atomic number $Z = 11$) is $v$. The velocity of an electron in its fifth orbit will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module