Calc Mass of Earth for Hydrogen Atmos Retention

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Homework Statement


calculate approximately how much more massive the Earth would have to be before it could retain a significant hydrogen atmosphere, assuming the Earth’s density to be the same as its current value.

Homework Equations


Temperature limit to retain hydrogen in the Earth's atmosphere: T «< 5042 (Mp/Rp ) *mn
Mp= ratio of mass of planet/body to Earth’s RE
Rp = ratio of radius of planet/body to Earth’s
mn= atomic mass number of gas particle

The Attempt at a Solution


not sure how to begin , any tips much appreciated
 
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izzy93 said:
not sure how to begin
Reread the question for starters --- what's showing in "relevant equations" does NOT look terribly correct/useful.
 
Thread 'Need help understanding this figure on energy levels'

Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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Thread 'Understanding how to "tack on" the time wiggle factor'

Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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