Miscalculation with speeds of electrons?

[asdf1]

for the following question:
how much work (in MeV) must be done to increase the speed of an electron from 1.2*10^8 m/s to 2.4*10^8 m/s?

my problem:
E= (gamma)mc^2=m(c^2){1/[1-(2.4/30^2]-1/[1-(1.2/30^2]}
=0.511(c^2)[1/(0.6)-1/(0.84)^(1/2)]=2.65*10^16

the correct answer should be 0.294 MeV~

does anybody know what went wrong?

 

[Andrew Mason]

for the following question:
how much work (in MeV) must be done to increase the speed of an electron from 1.2*10^8 m/s to 2.4*10^8 m/s?

my problem:
E= (gamma)mc^2=m(c^2){1/[1-(2.4/30^2]-1/[1-(1.2/30^2]}
=0.511(c^2)[1/(0.6)-1/(0.84)^(1/2)]=2.65*10^16

\Delta E = (\gamma_2 - \gamma_1)m_ec^2

\gamma_1 = (1-v_1^2/c^2)^{-1/2} = 1.091
\gamma_2 = (1-v_2^2/c^2)^{-1/2} = 1.667
m_ec^2 = .511 Mev

\Delta E = .576 * .511 = .294 MeV

AM

 

[asdf1]

i think I'm missing something...
m_ec^2 = .511 Mev
i thought that m_e=0.511?

 

[Doc Al]

m_e is the mass of the electron: 9.11 \ 10^{-31} kg. If you calculate m_e c^2 in standard units, you'll get the answer in Joules. Then convert Joules to eV. (1 eV = 1.60 \ 10^{-19} J.)

 

[Andrew Mason]

i think I'm missing something...
m_ec^2 = .511 Mev
i thought that m_e=0.511?

When mass is written in terms of an energy, it is understood that it is in units of Energy/c^2. The 1/c^2 is often omitted when it is written, so it can be confusing. So, m_e = .511 Mev/c^2 and m_ec^2 = .511 MeV.

AM

 

[asdf1]

my math is crummy...
um, isn't units and the numbers multiplied separately?
so m=(0.511*c^2) MeV?

 

[Andrew Mason]

my math is crummy...
um, isn't units and the numbers multiplied separately?
so m=(0.511*c^2) MeV?

Well, the units are really MeV/(9e16 m^2/sec^2) which works out to 1.78e-30 kilograms. But kilograms is not a very useful unit when measuring the mass of an electron. So we just use units of MeV/c^2 or MeV-mass

m \ne .511 c^2 MeV

m = .511 (MeV/c^2) units = .511 MeV(mass)
= .511e6/9e16 eV/m^2/sec^2 = .511e6/9e16 *1.6e(-19) kg

AM

 

[asdf1]

thank you! :)