A positive ion $A$ and a negative ion $B$ has charges $6.67 imes 10^{-19} \mathrm{C}$ and $9.6 imes 10^{-10} \mathrm{C}$, and masses $19.2 imes 10^{-27} \mathrm{~kg}$ and $9 imes 10^{-27} \mathrm{~kg}$ respectively. At an instant, the ions are separated by a certain distance r. At that…

Question

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19} \mathrm{C}$ and $9.6 \times 10^{-10} \mathrm{C}$, and masses $19.2 \times 10^{-27} \mathrm{~kg}$ and $9 \times 10^{-27} \mathrm{~kg}$ respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{45}$, where the value of 10$P$ is ________
(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$)
Assume that charge may not be an integral multiple of electrons.

Aicharya · Accepted Answer

$\begin{aligned}
F_e & =\frac{k q_1 q_2}{r^2} \\ F_g & =\frac{G m_1 m_2}{r^2} \\ \frac{F_e}{F_g} & =\frac{k q_1 q_2}{G m_1 m_2} \\ & =\frac{9 \times 10^9 \times 6.67 \times 10^{-19} \times 9.6 \times 10^{-10}}{6.67 \times 10^{-11} \times 19.2 \times 10^{-27} \times 9 \times 10^{-27}} \\ & =\frac{10^{-20}}{2 \times 10^{-65}}
\end{aligned}$

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19} \mathrm{C}$ and $9.6 \times…

Solution