Question:
The electric potential between a proton and an electron is r given by $V = V_0 in\frac{r}{r_0}, where r_0$ is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number.
The electric potential between a proton and an electron is r given by $V = V_0 in\frac{r}{r_0}, where r_0$ is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number.
Updated On: Jul 29, 2022
- $r_n?n$
- $r_n?\frac{1}{n}$
- $r_n?n^2$
- $r_n?\frac{1}{n^2}$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
$U=eV=eV_0 in\bigg(\frac{r}{r_0}\bigg)$
$|F|=\bigg|-\frac{dU}{dr}\bigg|=\frac{eV_0}{r}$
This force will provide the necessary centripetal force.
Hence, $\frac{mv^2}{r}=\frac{eV_0}{r}$
or $v=\sqrt{\frac{eV_0}{m}}$...(i)
Moreover, $mvr=\frac{nh}{2\pi}$...(ii)
Dividing E (ii) by (i), we have
or $r_n?n$
Was this answer helpful?
0
0
Top Questions on Electrostatic potential
- As shown in figure, a cuboid lies in a region with electric field \(E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} N / C\). The magnitude of charge within the cuboid is \(n \epsilon_0 C\). The value of \(n\) is _____. (if dimension of cuboid is \(1 \times 2 \times 3 m ^3\) )
- JEE Main - 2023
- Physics
- Electrostatic potential
- Three identical particle $A, B$ and$ C$ of mass $100 \,kg$ each are placed in a straight line with $AB = BC =13 \,m$ The gravitational force on a fourth particle $P$ of the same mass is $F$, when placed at a distance $13\, m$ from the particle B on the perpendicular bisector of the line $AC$ The value of $F$ will be approximately :
- JEE Main - 2023
- Physics
- Electrostatic potential
- Eight copper wire of length $l$ and diameter $d$ are joined in parallel to form a single composite conductor of resistance $R$ If a single copper wire of length $2 l$ have the same resistance $(R)$ then its diameter will be ______$d$
- JEE Main - 2023
- Physics
- Electrostatic potential
- Two parallel plate capacitors of capacity $C$ and $3 C$ are connected in parallel combination and charged to a potential difference $18\, V$ The battery is then disconnected and the space between the plates of the capacitor of capacity $C$ is completely filled with a material of dielectric constant $9$ The final potential difference across the combination of capacitors will be______ $V$
- JEE Main - 2023
- Physics
- Electrostatic potential
A point source of light is placed at the focus of a concave mirror. Consider only paraxial rays. The shapes of the wavefronts of incident and reflected lights respectively are:
- TS EAMCET - 2023
- Physics
- Electrostatic potential
View More Questions
Questions Asked in IIT JEE exam
- If the weight of an object on earth's surface is 400 N, then weight of the same particle at a depth \(\frac{R}{2}\) from surface would be (R is radius of earth)
- IIT JEE - 2023
- Stereoisomers
- For an electron and a proton (mp=1847 me) with same de-broglie wavelength, the ratio of linear momentum is equal to?
- IIT JEE - 2023
- Stereoisomers
- The major product of the following reaction is
- IIT JEE - 2022
- Hydrocarbons
- Let $ \alpha ( a) \, and \, \beta (a) $ be the roots of the equation $ (\sqrt [3] {1 + a} - 1) x^2 - (\sqrt {1 + a} - 1) x + (\sqrt [ 6] {1 + a} - 1) = 0$, where a > - 1. Then, $ lim_{a \to 0^+ } $, $ \alpha (a) \, and \, lim_{a \to 0^+ } \beta $ (a) are
- IIT JEE - 2012
- Quadratic Equations
- Let $f:(-1,1)\rightarrow$ R be such that $f(cos 4 \theta)=\frac{2}{2-sec^2 \theta}$ for $\theta \in \Bigg(0,\frac{\pi}{4}\Bigg)\cup\Bigg(\frac{\pi}{4},\frac{\pi}{2}\Bigg).$ Then, the value(s) of $f\Bigg(\frac{1}{3}\Bigg)$ is are
- IIT JEE - 2012
- Functions
View More Questions
Concepts Used:
Electrostatic Potential
The electrostatic potential is also known as the electric field potential, electric potential, or potential drop is defined as “The amount of work that is done in order to move a unit charge from a reference point to a specific point inside the field without producing an acceleration.”
SI Unit of Electrostatic Potential:
SI unit of electrostatic potential - volt
Other units - statvolt
Symbol of electrostatic potential - V or φ
Dimensional formula - ML2T3I-1
Electric Potential Formula:
The electric potential energy of the system is given by the following formula:
U = 1/(4πεº) × [q1q2/d]
Where q1 and q2 are the two charges that are separated by the distance d.