The ratio of centripetal acceleration for an | 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 a Bohr orbit is given by $a_c = \frac{v^2}{r}$.For a hydrogen atom, the velocity $v$ in the $

Vedclass · Accepted Answer

$625 : 81$

Vedclass · Answer

(C) The centripetal acceleration $a_c$ of an electron in a Bohr orbit is given by $a_c = \frac{v^2}{r}$.For a hydrogen atom, the velocity $v$ in the $n^{th}$ orbit is proportional to $\frac{1}{n}$ $(v \propto \frac{1}{n})$ and the radius $r$ is proportional to $n^2$ $(r \propto n^2)$.Substituting these into the formula for centripetal acceleration:$a_c \propto \frac{(1/n)^2}{n^2} = \frac{1/n^2}{n^2} = \frac{1}{n^4}$.Therefore, the ratio of centripetal acceleration for the $3^{rd}$ and $5^{th}$ orbits is:$\frac{a_3}{a_5} = \frac{n_5^4}{n_3^4} = \left(\frac{5}{3}\right)^4 = \frac{625}{81}$.Thus, the ratio is $625 : 81$.

The ratio of centripetal acceleration for an electron revolving in $3^{rd}$ and $5^{th}$ Bohr orbit of hydrogen atom is

Similar Questions

The ionization energy of a $Li^{++}$ ion is .......

The gyromagnetic ratio of an electron in a hydrogen atom,according to the Bohr model,is

The de-Broglie wavelength of the electron in the ground state of a hydrogen atom is ........ $\mathring{A}$.

If an electron is revolving in its Bohr orbit having Bohr radius of $0.529 Å$,then the radius of the third orbit is

The radius of the orbit of an electron in a hydrogen atom is $0.5 \ \mathring{A}$. The speed of the electron is $2 \times 10^6 \ m/s$. The current in the loop due to the motion of the electron is ............. $mA$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module