Identifying Particles by Mass: A High-Energy Physics Experiment

[tandoorichicken]

why u should not skip steps

In a high-energy physics experiment, a subnuclear particle moves in a circular arc of 0.27-m radius perpendicular to a magnetic field of 2.7*10^-2 T. The kinetic energy of the particle is determined to be 4.1*10^16 J. Identify the particle from its mass. The masses of the electron, pion, and proton are 9.1*10^-31 kg, 2.5*10^-28 kg, and 1.67*10^-27 kg, respectively. Assume that the particle is known to have a positive charge equal to the magnitude of the electron charge.

Okay, so I know r= 0.27, B= 2.7*10^-2, q= 1.6*10^-19 C, and KE= 4.1*10^-16 J. Now I need to find mass to id the particle.
$$KE = \frac{mv^2}{2}$$, so $$v = \sqrt{2m * (KE)}$$.
$$r = \frac{mv}{qB}$$, and then I subbed in the v from the kinetic energy equation.
$$r = \frac{m\sqrt{2m * (KE)}}{qB}$$
$$\frac{rqB}{\sqrt{2KE}} = m^{3/2}$$
m = 1.49*10^-9.

I really screwed this up didnt I? Was it a conceptual or a math error?

 

[tandoorichicken]

Crap.

So it was a dumb math error. Perfect example of why you shouldn't skip steps like I do.

$$KE = \frac{mv^2}{2} \rightarrow 2KE = mv^2 \rightarrow \frac{2KE}{m} = v^2 \rightarrow v = \sqrt{\frac{2KE}{m}}$$.

Remember guys, show all your work!
hehe,
Tchicken.

 

[tandoorichicken]

By the way, the particle is a proton.