Charge to Mass Ratio of a Particle to Electron - Mass

[5hassay]

Homework Statement

To start, I did find a few very similar or equal topics, but I could not gather enough information.
And, the pi symbols are intended to be pi symbols with negative superscripts (couldn't get it to work/finalize).

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The charge-to-mass ratio of a \pi^- particle is known to be 9. \times 10^{8} C/kg. The charge-to-mass ratio of an electron is given to be 1.76 \times 10^{11} C/kg. Which particle will have a greater mass based on their ratios? And, given that the value of the elementary charge is defined as e = 1.6 \times 10^{-19} C, calculate the mass of the \pi^- particle -- compare this mass to that of the electron.

Homework Equations

\frac{q}{m} = \frac{c}{B r}

where c is the speed of light, q is charge, m is mass, B is magnetic field strength (given to be 1.43 T), and, r is radius.

The Attempt at a Solution

For the first part, I argued that because the ratio of the \pi^- particle is less than that of the electron, the \pi^- particle would have a greater mass. My reasoning is that, by the given equation formatted as
\frac{q}{m} = \frac{\frac{c}{B}}{r}
, it can be observed that the greater the radii the lesser the ratio (quotient), and the lesser the radii the greater the ratio. Then, considering the basis of a charge-to-mass ratio, the larger the mass the lesser the ratio, and the lesser the mass the larger the ratio. Consequently, the greater the mass or radius the lesser the ratio -- in other words, the least ratio will have the greatest mass/radius. (I say mass or radius because the value of the mass can be considered as the value of the radius [as shown by the most recent equation].)

For the second part, I did the following:

\frac{q}{m} = 9. \times 10^{8} C/kg
m = \frac{q}{9. \times 10^{8} C/kg}
m = \frac{1.6 \times 10^{-19} C}{9. \times 10^{8} C/kg}
m = 2. \times 10^{-28} kg

So, the mass of the \pi^- particle is about 1000 times greater than that of the electron (m = 9.1164 \times 10^{-31} kg).

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I'd like to know if I did this correctly, because I do not feel entirely confident. Much appreciation (for any help)! :)

 

[Delphi51]

The second part looks great.
The argument for the first part is needlessly complicated; that formula with the magnetic field and radius in it does not apply. Simply use your
m = q/(q/m)
formula and argue that if q remains the same but q/m is smaller for the pi particle, then m comes out larger.

 

[5hassay]

The second part looks great.
The argument for the first part is needlessly complicated; that formula with the magnetic field and radius in it does not apply. Simply use your
m = q/(q/m)
formula and argue that if q remains the same but q/m is smaller for the pi particle, then m comes out larger.

Ah, okay, I understand. For the first part, that is much more simple, clear, and understandable. Thank you very much!