Author Topic: Units in the lecture notes  (Read 44 times)

Anonymous

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Units in the lecture notes
« on: 03. February 2021, 16:33:03 »
In equation 3.27, should the m-term in \( (2/3m)^{1/2} \) be in the denominator? Otherwise, I don't get the correct units for \( \lambda \).
Also, in table 3.1, it says that \( T_9 \) is in units of 10^9 K, but that means that the exponentials have weird units, when they should have no units at all? I don't get it. There also seems to be weird units in the remaining factors, giving different powers of K in each term

Frederik Clemmensen

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Re: Units in the lecture notes
« Reply #1 on: 03. February 2021, 17:42:26 »
I think you might be right about equation 3.27, I will have to check more thoroughly.

About table 3.1 and the \( T_9 \), what is meant is that \( T_9 = \frac{T}{10^9K} \), so \( T_9 \) itself is unitless.

Frederik Clemmensen

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Re: Units in the lecture notes
« Reply #2 on: 04. February 2021, 14:39:20 »
Ok, there is in fact a mistake in eq. 3.27. It is supposed to look like this:
\[
\lambda_{ik} = 4S(E_{max}) \frac{\left(\frac{2}{3m}\right)^{\frac{1}{2}} \left(\frac{b}{2}\right)^{\frac{1}{3}}}{\left(k_BT\right)^{\frac{2}{3}}} \exp\left(- \frac{3\left(\frac{b}{2}\right)^{\frac{2}{3}}}{\left(k_BT\right)^{\frac{1}{2}}} \right)
 \]