Mass of an accelerated electron?

In summary, an electron is accelerated through a potential difference of 31kV, gaining energy qV and causing its total mass to increase by m = m0 + qV/c^2."
  • #1
Tryhard2
2
0

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 :)
 
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  • #2
This is OK! The electron gains energy qV , so total energy will be: E = m0c2 +qV = m c2 or m = m0 + qV/c2
 
  • #3
when you say qV? is that QU? (columb times volt) or something else

so essentially I did what you describe in the end?
 
  • #4
Tryhard2 said:
is that QU?
Yes

Tryhard2 said:
so essentially I did what you describe in the end?
Yes, I just referred the reasoning for doing this...
 
  • #5


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.
 

FAQ: Mass of an accelerated electron?

What is the mass of an accelerated electron?

The mass of an accelerated electron is approximately 9.11 x 10^-31 kilograms. This is a very small mass, as electrons are considered to be subatomic particles.

How does the mass of an accelerated electron compare to the mass of a stationary electron?

The mass of an accelerated electron is the same as the mass of a stationary electron. According to Einstein's theory of relativity, mass and energy are equivalent, so the increase in kinetic energy of an accelerated electron does not change its mass.

Can the mass of an accelerated electron be measured?

Yes, the mass of an accelerated electron can be measured using various techniques, such as mass spectrometry or the mass-to-charge ratio in particle accelerators.

Does the mass of an accelerated electron change as it moves at different speeds?

The mass of an accelerated electron does not change as it moves at different speeds. This is due to the principle of mass-energy equivalence, where the mass of an object is a measure of its energy content.

How is the mass of an accelerated electron related to its acceleration?

The mass of an accelerated electron is not directly related to its acceleration. However, the acceleration of an electron can affect its energy and therefore its mass, as shown by Einstein's famous equation E=mc^2. This means that the more energy an electron has, the greater its mass will be.

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