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A spherical fragment of a molecular cloud (hydrogen) with mass M = 1.5 Mo and R = 6000 a.u. starts to collapse. The dissociation energy of H₂ is Do = 4.52 eV and the ionization energy of H is Xo = 13.6 eV. a) b) c) (p d) Derive and numerically evaluate the dissociation energy Ed of the cloud. Derive and numerically evaluate the ionization energy E; of the cloud. Derive and numerically evaluate the final radius Rf of the cloud. Derive and numerically evaluate the final temperature of the gas Tf.

A spherical fragment of a molecular cloud (hydrogen) with mass M = 1.5 Mo and R = 6000 a.u. starts to collapse. The dissociation energy of H₂ is Do = 4.52 eV and the ionization energy of H is Xo = 13.6 eV. a) b) c) (p d) Derive and numerically evaluate the dissociation energy Ed of the cloud. Derive and numerically evaluate the ionization energy E; of the cloud. Derive and numerically evaluate the final radius Rf of the cloud. Derive and numerically evaluate the final temperature of the gas Tf.

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### Collapsing Molecular Cloud Educational Exercise A spherical fragment of a molecular cloud (hydrogen) with mass \( M = 1.5 M_\odot \) and \( R = 6000 \) a.u. starts to collapse. The dissociation energy of \( H_2 \) is \( D_0 = 4.52 \) eV and the ionization energy of \( H \) is \( \chi_0 = 13.6 \) eV. a) Derive and numerically evaluate the dissociation energy \( E_d \) of the cloud. b) Derive and numerically evaluate the ionization energy \( E_i \) of the cloud. c) Derive and numerically evaluate the final radius \( R_f \) of the cloud. d) Derive and numerically evaluate the final temperature of the gas \( T_f \).
Transcribed Image Text:### Collapsing Molecular Cloud Educational Exercise A spherical fragment of a molecular cloud (hydrogen) with mass \( M = 1.5 M_\odot \) and \( R = 6000 \) a.u. starts to collapse. The dissociation energy of \( H_2 \) is \( D_0 = 4.52 \) eV and the ionization energy of \( H \) is \( \chi_0 = 13.6 \) eV. a) Derive and numerically evaluate the dissociation energy \( E_d \) of the cloud. b) Derive and numerically evaluate the ionization energy \( E_i \) of the cloud. c) Derive and numerically evaluate the final radius \( R_f \) of the cloud. d) Derive and numerically evaluate the final temperature of the gas \( T_f \).
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