Question

A singly charged 7Li ion has a mass of 1.16 10-26 kg. It is accelerated through a potential difference of 523 V and subsequently enters a uniform magnetic field of magnitude 0.370 T perpendicular to the ion's velocity. Find the radius of its path.

Answer 1

`R=0.023m`

Step-by-step explanation:

From the question we are told that:

Mass
`m=1.16*10^(-26)`

Potential difference
`V=523V`

Magnitude
`m=0.370 T`

Generally the equation for Velocity is mathematically given by

`(1)/(2)mv^2=ev`

`v=(2ev)/(m)`

`v=(2*1.6*10^(-19)*542)/(1.16*10^(-26))`

`v=12.22*10^4m/s`

Generally the equation for Force is mathematically given by

`F=qvBsin \theta`

Where

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

`F=m(v^2)/(R)sin\theta`

Therefore

`R=(mv)/(qB sin \theta)`

`R=(1.6*10^(-26)*12.2*10^(4))/(1.60*10^(-19)*0.394 sin 90)`

`R=0.023m`