Charge to Mass Ratio of a Particle to Electron - Mass

In summary, the charge-to-mass ratio of a $\pi$- particle is known to be $9. \times 10^{8} C/kg$, while the charge-to-mass ratio of an electron is $1.76 \times 10^{11} C/kg$. Using the formula $m = q/(q/m)$, it can be argued that since the ratio of the $\pi$- particle is smaller, it would have a greater mass. For the second part, the mass of the $\pi$- particle was calculated to be about 1000 times greater than that of the electron.
  • #1
5hassay
82
0

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)! :)
 
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  • #2
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.
 
  • #3
Delphi51 said:
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!
 

What is the charge to mass ratio of a particle to electron-mass?

The charge to mass ratio of a particle to electron-mass is the ratio of the electric charge of a particle to its mass. It is commonly represented by the symbol "e/m" and has a value of approximately 1.75882 x 10^11 coulombs per kilogram.

How is the charge to mass ratio of a particle to electron-mass determined?

The charge to mass ratio of a particle to electron-mass can be determined through various methods, such as the deflection of particles in a magnetic field or the measurement of the frequency of a particle's cyclotron motion. These methods use the principles of electromagnetism and can provide accurate values for the charge to mass ratio.

Why is the charge to mass ratio of a particle to electron-mass important in physics?

The charge to mass ratio of a particle to electron-mass is important in physics because it helps to identify and classify different particles based on their properties. It also plays a crucial role in understanding the behavior of charged particles in electric and magnetic fields, which is essential in many areas of physics, including particle physics and astrophysics.

What is the difference between the charge to mass ratio of a particle and the mass of a particle?

The charge to mass ratio of a particle and the mass of a particle are two different properties of a particle. The charge to mass ratio is a ratio of the electric charge to mass, while the mass of a particle is a measure of the amount of matter contained within the particle. These two properties are not directly related, and a particle can have different charges and masses.

Can the charge to mass ratio of a particle to electron-mass change?

The charge to mass ratio of a particle to electron-mass is a fundamental property of a particle and is not expected to change. However, in certain situations, such as extreme temperatures or energy levels, particles can undergo transformations that can alter their charge to mass ratio. These changes are typically studied in high-energy physics experiments and are not observed in everyday phenomena.

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