Answer:
t = 4.21x10⁻⁷ s
Explanation:
The time (t) can be found using the angular velocity (ω):
[tex] \omega = \frac{\theta}{t} [/tex]
Where θ: is the angular displacement = π (since it moves halfway through a complete circle)
We have:
[tex] t = \frac{\theta}{\omega} = \frac{\theta}{v/r} [/tex]
Where:
v: is the tangential speed
r: is the radius
The radius can be found equaling the magnetic force with the centripetal force:
[tex] qvB = \frac{mv^{2}}{r} \rightarrow r = \frac{mv}{qB} [/tex]
Where:
m: is the mass of the alpha particle = 6.64x10⁻²⁷ kg
q: is the charge of the alpha particle = 2*p (proton) = 2*1.6x10⁻¹⁹C
B: is the magnetic field = 0.155 T
Hence, the time is:
[tex] t = \frac{\theta*r}{v} = \frac{\theta}{v}*\frac{mv}{qB} = \frac{\theta m}{qB} = \frac{\pi * 6.64 \cdot 10^{-27} kg}{2*1.6 \cdot 10^{-19} C*0.155 T} = 4.21 \cdot 10^{-7} s [/tex]
Therefore, the time that takes for an alpha particle to move halfway through a complete circle is 4.21x10⁻⁷ s.
I hope it helps you!
