Comparing Electron Mass in Different Speeds

[wilson_chem90]

Homework Statement

An electron has a rest mass of 9.11 x 10^-31 kg. The speed of the electron in the cathode ray tube of your computer monitor is 4.00 x 10^7 m/s. However, the speed of the electron is 0.98 c in a particle accelerator used in cancer therapy. How many times heavier is the electron in the particle accelerator than in the computer monitor?

Homework Equations

m = mo/ sqrt(1 - v^2/c^2)

The Attempt at a Solution

mo1 = m sqrt(1 - v^2/c^2)
= (9.11 x 10^-31 kg) sqrt{ 1 - (4.00 x 10^7 m/s)^2/(3.00 x 10^8 m/s)^2}
= (9.11 x 10^-31 kg) sqrt(0.017777777)
= (9.11 x 10-31 kg)(0.13333333)
= 1.21 x 10^-31 kg

mo2 = (9.11 x 10-31 kg) sqrt{1 - (0.98 c)2/c^2}
= (9.11 x 10-31 kg)(0.198997)
= 1.81 x 10^-31 kg

(1.81 x 10^-31 kg)/(1.21 x 10^-31 kg)
= 1.496 times

Therefore the electron is approx. 1.5 times heavier in the particle accelerator than it is in the computer monitor.


Is this correct?
Thanks

 

[w3390]

Your equations are correct but I am getting different values for mo1 and mo2 than you. For your value of mo1, you forgot to do 1 minus (4.00 x 10^7 m/s)^2/(3.00 x 10^8 m/s)^2. Instead you just took the second quantity and took the square root. For mo2, it looks correct, but when I calculate it I get a different answer. Maybe retype all the numbers into your calculator again and see if it was a typing error.

 

[wilson_chem90]

did you get (9.03 x 10^-31 kg) for m1? and (1.81 x 10^-31 kg) for m2?

 

[wilson_chem90]

but now it doesn't make sense, cause those answers are suggesting that the electron is heavier in the computer monitor than the particle accelerator

 

[wilson_chem90]

i just realized why this whole thing is completely wrong. i need to find m, not mo so the equation is completely wrong.

the equation is m = mo/ sqrt(1 - v^2/c^2)

so when i put all the numbers in for both sides

m1 = 9.19 x 10^-31 kg
m2 = 4.58 x 10^-31 kg

but still m2 should be heavier cause its in a particle accelerator, and the speed is much more significant..

 

[w3390]

Your m2 should be 4.58 x 10^-30 kg. Your off by an order of magnitude.

 

[wilson_chem90]

i see that now, sorry, thanks for helping me, honestly.