Mass of an accelerated electron?

[Tryhard2]

Homework Statement

An electron is accelerated from rest through a potential difference of 31kV

Homework Equations

I don't know how to engage or solve a problem like this, I've done this attempt but I'm very uncertain that I've done it in a correct way, it's hard to understand if I've choosen correct forumulas etc it feels much like guesswork for me, but the final answer seem plausible as it is a small increase as it should, shouldn't it?

Have I done it right and have a good solution? if not, how do you solve such a problem?

My feeling was that if there is a mass while rest and another for acceleration I can add them together like this. But I'm not sure I have the right masses even.

The Attempt at a Solution

the electrons mass, m_0 = 9.109*10^-31 kg
Speed of light, c = 2.998*10^8 m/s

E=m_1*c^2 and E=QU give me:
m_1 = QU / c^2

m_1 = (1.602*10^-19) * 31000 / (2.998*10^8)^2 = 5.525*10^-32 kg

I then add m_1 and m_0 together giving me my final answer. m, m= m_0 + m_1
m = (5.525*10^-32) + (9.109*10^-31) = 9.66*10^-31 kg

Very thankful for input :)

 

[cosmic dust]

This is OK! The electron gains energy qV , so total energy will be: E = m₀c² +qV = m c² or m = m₀ + qV/c²

 

[Tryhard2]

when you say qV? is that QU? (columb times volt) or something else

so essentially I did what you describe in the end?

 

[cosmic dust]

is that QU?

Yes

so essentially I did what you describe in the end?

Yes, I just referred the reasoning for doing this...

 

[Nickie]

I would like to point out that your solution is not entirely correct. The equation E=mc^2 only applies to objects at rest, so it cannot be used to calculate the mass of an accelerated electron. Additionally, the equation E=QU is also incorrect, as it does not take into account the kinetic energy of the electron.

To solve this problem, we can use the equation KE=1/2mv^2, where KE is the kinetic energy, m is the mass of the electron, and v is the velocity. We can also use the equation V=KE/q, where V is the potential difference, KE is the kinetic energy, and q is the charge of the electron.

Plugging in the given values, we get KE=1/2mv^2=31kV, and V=KE/q=31kV. Solving for v, we get v=√(2qV/m). Plugging in the values for q (1.602*10^-19 C), V (31kV), and m (9.109*10^-31 kg), we get v=1.37*10^8 m/s.

Using the equation E=mc^2, we can now calculate the mass of the accelerated electron. E=KE=1/2mv^2, so m=2KE/v^2. Plugging in the values for KE (31kV), v (1.37*10^8 m/s), and c (2.998*10^8 m/s), we get m=3.25*10^-31 kg.

Therefore, the mass of the accelerated electron is 3.25*10^-31 kg, which is slightly larger than the rest mass of the electron (9.109*10^-31 kg). This is because the electron has gained kinetic energy and therefore, its total energy and mass have increased.