The ratio of the centripetal accelerations of | vedclass

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

Question

(C) The centripetal acceleration $a_c$ of an electron in the $n$-th orbit is given by $a_c = \frac{v^2}{r}$. Since $v \propto \frac{1}{n}$ and $r \pro

Vedclass · Accepted Answer

$\frac{h}{2 \pi}$

Vedclass · Answer

(C) The centripetal acceleration $a_c$ of an electron in the $n$-th orbit is given by $a_c = \frac{v^2}{r}$. Since $v \propto \frac{1}{n}$ and $r \propto n^2$,we have $a_c \propto \frac{(1/n)^2}{n^2} = \frac{1}{n^4}$.Given the ratio of centripetal accelerations for two successive orbits $n$ and $n-1$ is $81:16$,we have $\frac{a_c(n-1)}{a_c(n)} = \frac{n^4}{(n-1)^4} = \frac{81}{16} = (\frac{3}{2})^4$.Thus,$n=3$ and $n-1=2$.The angular momentum of an electron in the $n$-th orbit is $L_n = \frac{nh}{2\pi}$.The change in angular momentum during the transition between these two states is $\Delta L = L_3 - L_2 = \frac{3h}{2\pi} - \frac{2h}{2\pi} = \frac{h}{2\pi}$.

The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to a transition between these two states,the angular momentum of the electron changes by ($h$ - Planck's constant).

Similar Questions

The third line of the Balmer series of an ion equivalent to a hydrogen atom has a wavelength of $108.5 \ nm$. The ground state energy of an electron of this ion will be.....$eV$

Speed of electron in its $1^{st}$ Bohr's orbit is given by $2.18 \times 10^6 \ m/s$. If the time period of electron in $n^{th}$ orbit is measured as $4.10 \ fs$,the value of $n$ is

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?

The gravitational force between a $H$-atom and another particle of mass $m$ is given by Newton's law $F = G\frac{M m}{r^2}$. Here,$M$ represents:

When the electron orbiting in a hydrogen atom in its ground state moves to the third excited state, the de-Broglie wavelength associated with it

Vedclass Test Series

Exam Paper Generator

Online Exam Module