If the electron of a hydrogen atom is present | vedclass

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

Question

(C) The kinetic energy $(KE)$ of an electron in an orbit is given by $KE = \frac{1}{2}mv^2$. From the electrostatic force balance,the centripetal forc

Vedclass · Accepted Answer

$\frac{-e^2}{2r}$

Vedclass · Answer

(C) The kinetic energy $(KE)$ of an electron in an orbit is given by $KE = \frac{1}{2}mv^2$. From the electrostatic force balance,the centripetal force is provided by the Coulombic attraction: $\frac{mv^2}{r} = \frac{e^2}{r^2}$,which implies $mv^2 = \frac{e^2}{r}$. Substituting this into the $KE$ expression: $KE = \frac{1}{2} 	imes \frac{e^2}{r} = \frac{e^2}{2r}$. The potential energy $(PE)$ of the electron is given by $PE = \frac{-e^2}{r}$. The total energy $(E)$ is the sum of kinetic and potential energy: $E = KE + PE = \frac{e^2}{2r} - \frac{e^2}{r} = \frac{-e^2}{2r}$.

If the electron of a hydrogen atom is present in the first orbit,the total energy of the electron is

Similar Questions

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$,then $(\tan \alpha, \tan \beta)$ is equal to

During the depression of freezing point in a solution,which of the following are in equilibrium?

If $|a| < 1$ and $b = \sum_{k=1}^{\infty} \frac{a^k}{k}$,then $a$ is equal to

Consider two reactions:
$I$. $Zn +$ conc. $HNO_3$ (hot) $\to Zn(NO_3)_2 + X + H_2O$
$II$. $Zn +$ dil. $HNO_3$ (cold) $\to Zn(NO_3)_2 + Y + H_2O$
Compounds $X$ and $Y$ are respectively:

The heating of $NH _4 NO _2$ at $60-70^{\circ} C$ and $NH _4 NO _3$ at $200-250^{\circ} C$ is associated with the formation of nitrogen containing compounds $X$ and $Y$, respectively. $X$ and $Y$, respectively, are

Vedclass Test Series

Exam Paper Generator

Online Exam Module