A nucleus at rest undergoes alpha- decay acco | vedclass

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

Question

(B) The $\alpha-$ particle moves in a region with $\vec{E} = E_0 \hat{i}$ and $\vec{B} = B_0 \hat{i}$. The electric force $\vec{F}_E = q_{\alpha} E_0

Vedclass · Accepted Answer

$10^7 \ m/s$

Vedclass · Answer

(B) The $\alpha-$ particle moves in a region with $\vec{E} = E_0 \hat{i}$ and $\vec{B} = B_0 \hat{i}$. The electric force $\vec{F}_E = q_{\alpha} E_0 \hat{i}$ acts along the $x-$axis,causing acceleration $a_x = \frac{q_{\alpha} E_0}{m_{\alpha}}$. The magnetic force $\vec{F}_B = q_{\alpha} (\vec{v} 	imes \vec{B})$ is perpendicular to the velocity and the magnetic field,so it does no work and does not change the speed.At time $t$,the velocity component along the $x-$axis is $v_x = a_x t = \left( \frac{q_{\alpha} E_0}{m_{\alpha}} ight) \left( \sqrt{3} 	imes 10^7 \frac{m_{\alpha}}{q_{\alpha} E_0} ight) = \sqrt{3} 	imes 10^7 \ m/s$.The velocity component along the $y-$axis remains constant at $v_y = v_0$.The final speed $v_f$ is given as $2v_0$. Thus,$v_f^2 = v_x^2 + v_y^2 = (2v_0)^2 = 4v_0^2$.Substituting the values: $(\sqrt{3} 	imes 10^7)^2 + v_0^2 = 4v_0^2$.$3 	imes 10^{14} = 3v_0^2 \implies v_0^2 = 10^{14} \implies v_0 = 10^7 \ m/s$.

Similar Questions

The magnifying power of a telescope is $9$. When it is adjusted for parallel rays,the distance between the objective and the eye-piece is found to be $20\, cm$. The focal lengths of the two lenses are

When is the '$DUB$' sound heard during the cardiac cycle?

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three vectors such that $\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi}{2}$,then:

If the straight lines $2x + 3y - 1 = 0$,$x + 2y - 1 = 0$ and $ax + by - 1 = 0$ form a triangle with the orthocentre at the origin,then $(a, b) =$

Which one of the following orders is not in accordance with the property stated against it?

Vedclass Test Series

Exam Paper Generator

Online Exam Module