- #1
5hassay
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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 [tex]\pi[/tex]- particle is known to be [tex] 9. \times 10^{8} C/kg [/tex]. The charge-to-mass ratio of an electron is given to be [tex] 1.76 \times 10^{11} C/kg [/tex]. Which particle will have a greater mass based on their ratios? And, given that the value of the elementary charge is defined as [tex] e = 1.6 \times 10^{-19} C [/tex], calculate the mass of the [tex]\pi[/tex]- particle -- compare this mass to that of the electron.
Homework Equations
[tex] \frac{q}{m} = \frac{c}{B r} [/tex]
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 [tex]\pi[/tex]- particle is less than that of the electron, the [tex]\pi[/tex]- particle would have a greater mass. My reasoning is that, by the given equation formatted as
[tex] \frac{q}{m} = \frac{\frac{c}{B}}{r} [/tex]
, 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:
[tex] \frac{q}{m} = 9. \times 10^{8} C/kg [/tex]
[tex] m = \frac{q}{9. \times 10^{8} C/kg} [/tex]
[tex] m = \frac{1.6 \times 10^{-19} C}{9. \times 10^{8} C/kg} [/tex]
[tex] m = 2. \times 10^{-28} kg [/tex]
So, the mass of the [tex]\pi[/tex]- particle is about 1000 times greater than that of the electron ([tex] m = 9.1164 \times 10^{-31} kg [/tex]).
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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)! :)