In an atom,two electrons move around the nucl | vedclass

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

Question

(C) The time period $T$ for an electron in a circular orbit is given by $T = \frac{2 \pi r}{v}$.According to Bohr's theory,the radius $r \propto n^{2}

Vedclass · Accepted Answer

$1 : 8$

Vedclass · Answer

(C) The time period $T$ for an electron in a circular orbit is given by $T = \frac{2 \pi r}{v}$.According to Bohr's theory,the radius $r \propto n^{2}$ and the velocity $v \propto \frac{1}{n}$.Substituting these into the expression for $T$,we get $T \propto \frac{r}{v} \propto \frac{n^{2}}{1/n} = n^{3}$.Since $r \propto n^{2}$,we have $n \propto r^{1/2}$,so $T \propto (r^{1/2})^{3} = r^{3/2}$.Therefore,the ratio of the time periods is $\frac{T_{1}}{T_{2}} = \left(\frac{R_{1}}{R_{2}}\right)^{3/2}$.Given $R_{1} = R$ and $R_{2} = 4R$,we have $\frac{T_{1}}{T_{2}} = \left(\frac{R}{4R}\right)^{3/2} = \left(\frac{1}{4}\right)^{3/2} = \frac{1}{8}$.The ratio is $1 : 8$.

In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is:

Similar Questions

The height at which the weight of a body becomes $\frac{1}{9}^{th}$ of its weight on the surface of the Earth (radius of Earth $R$) is:

What is the equivalent capacitance of the system of capacitors between $A$ and $B$?

What is obtained when gypsum is heated at $300\,^oC$?

If $z$ is a complex number satisfying $|z - 3| \leq 5$,then the range of $|z + 3i|$ is (where $i = \sqrt{-1}$)

$A$ capacitor $C = 100 \ \mu F$ is connected to three resistors,each of resistance $1 \ k\Omega$,and a battery of emf $9 \ V$. The switch $S$ has been closed for a long time to charge the capacitor. When switch $S$ is opened,the capacitor discharges with a time constant of.....$ms$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module