A proton,an electron,and a Helium nucleus hav | vedclass

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

Question

(D) The radius of a charged particle moving in a magnetic field is given by $r = \frac{mv}{qB}$.Since kinetic energy $K = \frac{1}{2}mv^2$,we have $mv

Vedclass · Accepted Answer

$r_e < r_p = r_{He}$

Vedclass · Answer

(D) The radius of a charged particle moving in a magnetic field is given by $r = \frac{mv}{qB}$.Since kinetic energy $K = \frac{1}{2}mv^2$,we have $mv = \sqrt{2mK}$.Substituting this into the radius formula,we get $r = \frac{\sqrt{2mK}}{qB}$.Given that $K$ and $B$ are the same for all particles,$r \propto \frac{\sqrt{m}}{q}$.For a proton $(p)$: $m_p = m, q_p = e$,so $r_p \propto \frac{\sqrt{m}}{e}$.For an electron $(e)$: $m_e \approx \frac{m}{1836}, q_e = e$,so $r_e \propto \frac{\sqrt{m/1836}}{e} = \frac{r_p}{\sqrt{1836}}$. Thus,$r_e For a Helium nucleus $(He^{2+})$: $m_{He} \approx 4m, q_{He} = 2e$,so $r_{He} \propto \frac{\sqrt{4m}}{2e} = \frac{2\sqrt{m}}{2e} = \frac{\sqrt{m}}{e} = r_p$.Therefore,$r_e < r_p = r_{He}$.

$A$ proton,an electron,and a Helium nucleus have the same kinetic energy. They are moving in circular orbits in a plane due to a magnetic field perpendicular to the plane. Let $r_p, r_e$,and $r_{He}$ be their respective radii. Then:

Similar Questions

If a proton enters perpendicularly into a magnetic field with velocity $v$,the time period of revolution is $T$. If the proton enters with velocity $2v$,what will be the time period?

$A$ charged particle of mass $m$ and charge $q$ is projected with velocity $v$ into a region of uniform magnetic field $B$ confined between two parallel plates separated by a distance $d$,as shown in the figure. What is the condition for the charged particle not to strike the opposite plate?

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $B = B_0 \hat{k}$.

$A$ proton, a deuteron (nucleus of ${ }_1 H^2$) and an $\alpha$-particle with the same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is:

The ratio of time periods of $\alpha$-particle and proton moving on circular path in a uniform magnetic field is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module