A nucleus with energy frac{1}{2}mv^2 is fired | vedclass

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

Question

(B) At the distance of closest approach $(r)$,the initial kinetic energy of the projectile is completely converted into electrostatic potential energy

Vedclass · Accepted Answer

$1/m$

Vedclass · Answer

(B) At the distance of closest approach $(r)$,the initial kinetic energy of the projectile is completely converted into electrostatic potential energy.The initial kinetic energy is $K = \frac{1}{2}mv^2$.The electrostatic potential energy at distance $r$ is $U = \frac{k(Ze)(2e)}{r}$,where $2e$ is the charge of the alpha particle (assuming it is an alpha particle as is standard in Rutherford scattering problems).Equating the two:$\frac{1}{2}mv^2 = \frac{k(Ze)(2e)}{r}$Rearranging for $r$:$r = \frac{4kZe^2}{mv^2}$From this expression,we can see that $r \propto \frac{1}{m}$ and $r \propto \frac{1}{v^2}$.Comparing this with the given options,the correct proportionality is $r \propto 1/m$.

$A$ nucleus with energy $\frac{1}{2}mv^2$ is fired at a target nucleus of charge $Ze$. The distance of closest approach to the $Ze$ nucleus is proportional to which of the following?

Similar Questions

According to classical theory,the Rutherford atom was:

State the postulates of Dalton's atomic theory.

$A$ neutron collides head-on with a stationary hydrogen atom in its ground state. Which of the following statements are correct? (Assume that the hydrogen atom and neutron have the same mass):

Which one did Rutherford consider to be supported by the results of experiments in which $\alpha - $ particles were scattered by gold foil?

In the Geiger-Marsden experiment,which of the following is used to calculate the trajectory of the $\alpha$-particle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module