The effective mass of an electron, due to special relativity, lower than the real mass. So I thought one can calculate from the mass ratio the velocity as it is dependent by a factor of $\sqrt{1-v^2/c^2}=m^*/m_e$. I stole from this the $v^2$ term and plugged it into $E_k=\frac{m_e v^2}{2}$ to get $$E_k=\frac{m_e c^2 (1-(m^*/m_e)^2)}{2}$$. When I plug in mass ratios like 0.1, 0.5 or other common ratios, I received values in range of thousands of electron volts, which is problematic when insulators have only a bandgap of a handfull electron volts. When I look on wikipedia I see the equation for total energy being $$E=\frac{m_e c^2}{\sqrt{1-v^2/c^2}}$$, but using that equation I get values even higher. Where did I go wrong?
$\begingroup$
$\endgroup$
5
-
$\begingroup$ The relativistic mass is not lower than the mass of the e not moving or what do you call me and m* $\endgroup$– trulaCommented Jul 20, 2023 at 9:55
-
$\begingroup$ hello @trula I now realize that the wikipedia article states $m_e/m^*=\sqrt{1-v^2/c^2}$ instead of the other way around but that confuses me more, as it at the same time states that the effective mass of the electron is changed due to special relativity. Most materials I have looked at in papers have an effective electron mass below that of the electron at rest. $\endgroup$– maxsiegCommented Jul 20, 2023 at 10:06
-
$\begingroup$ Have you read this ? en.wikipedia.org/wiki/Effective_mass_(solid-state_physics) ." the effective mass is usually stated as a factor multiplying the rest mass of an electron, me $(9.11 × 10^{−31 kg})$. This factor is usually in the range 0.01 to 10, but can be lower or higher" $\endgroup$– anna vCommented Jul 20, 2023 at 10:53
-
$\begingroup$ that article is useful thanks @annav . I also saw on a different question the suggestion to look at ISBN 0201079569 to check how mass of electron is calculated, which i am currently reading. $\endgroup$– maxsiegCommented Jul 20, 2023 at 11:16
-
$\begingroup$ Where did you find "Most materials I have looked at in papers have an effective electron mass below that of the electron at rest" quote at least one relevant paper! $\endgroup$– trulaCommented Jul 21, 2023 at 13:50
Add a comment
|