A proton, a deuteron, and an alpha-particle e | vedclass

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

Question

(A) The radius of the circular path of a charged particle in a magnetic field is given by $r = \frac{mv}{qB}$.Since kinetic energy $E = \frac{1}{2}mv^

Vedclass · Accepted Answer

$r_\alpha = r_p < r_d$

Vedclass · Answer

(A) The radius of the circular path of a charged particle in a magnetic field is given by $r = \frac{mv}{qB}$.Since kinetic energy $E = \frac{1}{2}mv^2$, we have $mv = \sqrt{2mE}$.Substituting this into the radius formula, we get $r = \frac{\sqrt{2mE}}{qB}$.Given that $E$ and $B$ are the same for all particles, we have $r \propto \frac{\sqrt{m}}{q}$.For a proton $(p)$: mass $= m$, charge $= e$. So, $r_p \propto \frac{\sqrt{m}}{e}$.For a deuteron $(d)$: mass $= 2m$, charge $= e$. So, $r_d \propto \frac{\sqrt{2m}}{e}$.For an $\alpha$-particle $(\alpha)$: mass $= 4m$, charge $= 2e$. So, $r_\alpha \propto \frac{\sqrt{4m}}{2e} = \frac{2\sqrt{m}}{2e} = \frac{\sqrt{m}}{e}$.Comparing the ratios: $r_p : r_d : r_\alpha = 1 : \sqrt{2} : 1$.Therefore, $r_p = r_\alpha < r_d$.

$A$ proton, a deuteron, and an $\alpha$-particle enter a region of a uniform magnetic field perpendicular to their velocities with the same kinetic energy. If $r_p, r_d,$ and $r_\alpha$ are the radii of the circular paths of these particles, respectively, then:

Similar Questions

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

$A$ strong magnetic field is applied on a stationary electron,then

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

$A$ charge $q_0$ moving with velocity $\overrightarrow{v}$ in a magnetic field of induction $\overrightarrow{B}$ experiences a force $\overrightarrow{F}$. The angle between $\overrightarrow{v}$ and $\overrightarrow{B}$ is $\theta$. The speed of $q_0$ after one second will be

An electron is travelling in the east direction and a magnetic field is applied in the upward direction. In which direction will the electron deflect?

Vedclass Test Series

Exam Paper Generator

Online Exam Module