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:

From a carbon nanotube of $1 \,\mu m$ length and $1 \,nm$ radius,$10$ electrons have been removed. Assume the resulting positive charge to be distributed uniformly over the surface of the tube. The energy of an electron moving in a stable circular orbit around the axis along the length of the tube is calculated by applying the Bohr model. Accordingly,the frequency of radiation required to excite an electron from its ground state to the next level is in the range of (charge of the electron,$e = 1.60 \times 10^{-19} \,C$; mass of the electron,$m_e = 9.11 \times 10^{-31} \,kg$; Planck's constant,$h = 6.63 \times 10^{-34} \,Js$; Permittivity of free space,$\varepsilon_0 = 8.85 \times 10^{-12} \,F/m$)

Angular momentum of an electron in a hydrogen atom is $\frac{3h}{2\pi}$. The wavelength of this electron is approximately $...... \mathring{A}$.

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

In accordance with Bohr's model,find the quantum number that characterizes the Earth's revolution around the Sun in an orbit of radius $1.5 \times 10^{11} \; m$ with an orbital speed of $3 \times 10^{4} \; m/s$. (Mass of Earth $= 6.0 \times 10^{24} \; kg$)

An electron in a hydrogen atom undergoes a transition from a higher energy level to a lower energy level. The incorrect statement of the following is