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

If the direction of the initial velocity of the charged particle is neither along nor perpendicular to that of the magnetic field,then the orbit will be

The following figure shows the path of an electron that passes through two regions containing uniform magnetic fields of magnitudes $B_1$ and $B_2$. Its path in each region is a half-circle. Choose the correct option.

$A$ charged particle moves through a magnetic field in a direction perpendicular to it. Then the

In an experiment,electrons are accelerated from rest by applying a voltage of $500 \, V$. Calculate the radius of the path if a magnetic field of $100 \, mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19} \, C$,Mass of the electron $= 9.1 \times 10^{-31} \, kg$]

Two charged particles,having the same kinetic energy,are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of the radii of their circular paths is $6:5$ and their respective masses ratio is $9:4$,then the ratio of their charges will be.

Vedclass Test Series

Exam Paper Generator

Online Exam Module