Question

What is the answer to part B? Must be in 3 significant digits.

Answer 1

As the exercice tells us, the magnetic force will act as a centripetal force. The equation which gives us the centripetal acceleration in this case is the following:

`a_(cp)=(qvB)/(m)`

By replacing the acceleration part we get:

`(v^2)/(R)=(qvB)/(m)`

Speeding up a bit, we can isolate R in the following manner

`R=(mv)/(qB)`

Where R is the radius, m is the mass, v is the velocity, q is the charge of the particle, and B is the magnetic field

The next thing we need to take into account is our particle. As it is an alpha particle, it has two protons and two neutrons. This tells us that its mass is:

`m=4*m_p=4*m_n=4*1.67*10^(-27)=6.68*10^(-27)`

And its charge, which is:

`q=2*1.6*10^(-19)=3.2*10^(-19)`

As we only have two charged particles, and the charge of each individual proton is 1.6*10^(-19) C

Finally, with all this information, we can get:

`R=(6.68*10^(-27)*9.7*10^6)/(3.2*10^(-19)*1.44)=0.141m`

(Note: The velocity of 9.7*10^6 was given by the exercise)