To calculate the size of a hydrogen ion (H^-) | vedclass

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

Question

(B) Let the velocity of the electron be $v$.The angular momentum of each electron is given as $mvr = \hbar$.The net electrostatic force acting on one

Vedclass · Accepted Answer

$\frac{4}{3} a_B$

Vedclass · Answer

(B) Let the velocity of the electron be $v$.The angular momentum of each electron is given as $mvr = \hbar$.The net electrostatic force acting on one electron is the attraction from the nucleus minus the repulsion from the other electron. Since the electrons are on opposite sides,the distance between them is $2r$.$F_e = \frac{e^2}{4\pi\varepsilon_0 r^2} - \frac{e^2}{4\pi\varepsilon_0(2r)^2} = \frac{e^2}{4\pi\varepsilon_0 r^2} - \frac{e^2}{16\pi\varepsilon_0 r^2} = \frac{3}{4} \frac{e^2}{4\pi\varepsilon_0 r^2}$.The centripetal force required for circular motion is $F_c = \frac{mv^2}{r} = \frac{(mvr)^2}{mr^3} = \frac{\hbar^2}{mr^3}$.Equating the forces,$F_c = F_e$:$\frac{\hbar^2}{mr^3} = \frac{3}{4} \frac{e^2}{4\pi\varepsilon_0 r^2}$.Solving for $r$:$r = \frac{4}{3} \left( \frac{4\pi\varepsilon_0\hbar^2}{me^2} \right) = \frac{4}{3} a_B$.

Similar Questions

$A$ beam of monochromatic light is used to excite the electron in $Li^{++}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 10^{-10} \; m$. The value of $x$ is $\dots$. [Given $hc = 1242 \; eV \cdot nm$]

In a Bohr atom,the total energy of an electron in the $n$-th allowed orbit is $E_n$ and its angular momentum is $J_n$. Then:

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level $n$ to level $(n-1)$. For large $n$,show that this frequency equals the classical frequency of revolution of the electron in the orbit.

Assume that there is no repulsive force between the electrons in an atom,but the force between positive and negative charges is given by Coulomb's law as usual. Under such circumstances,calculate the ground state energy of a $He$ atom.

When a hydrogen atom emits a photon of energy $12.09 \,eV$,its orbital angular momentum changes by (where $h$ is Planck's constant)

Vedclass Test Series

Exam Paper Generator

Online Exam Module