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) According to Bohr's theory,the radius of an orbit is $r \propto n^{2}$ and the velocity of an electron is $v \propto \frac{1}{n}$.Time period $T$

Vedclass · Accepted Answer

$1 : 8$

Vedclass · Answer

(C) According to Bohr's theory,the radius of an orbit is $r \propto n^{2}$ and the velocity of an electron is $v \propto \frac{1}{n}$.Time period $T$ is given by $T = \frac{2 \pi r}{v}$.Substituting the proportionality relations,$T \propto \frac{n^{2}}{1/n} = n^{3}$.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 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 get $\frac{T_{1}}{T_{2}} = \left(\frac{R}{4R}\right)^{3/2} = \left(\frac{1}{4}\right)^{3/2} = \frac{1}{8}$.

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

In the hydrogen spectrum,the energy during the first Lyman transition is $E = 10.2 \ eV$. The same energy is observed during the second Balmer series transition in which of the following species?

What is the radius of the stationary orbits $(n)$? State the formula.

$1$ mole of photons, each of frequency $2500 \ s^{-1}$, would have approximately a total energy of:

Which of the following energy changes is less than the third Balmer transition in the $He^{\oplus}$ ion?

Which of the following is correct for the Humphrey series of the hydrogen spectrum?

Vedclass Test Series

Exam Paper Generator

Online Exam Module