Intro to astrophysics:
(a) somewhere in our galaxy resides a cloud of neutral hydrogen gas with a radius r. the gas density is n. (a) show that the number of 21-cm photons the cloud emits every second is given by:
n_{ph}=\frac{\pi r^{3}n}{t}
(b) if the cloud is a distance d from the sun, show that the energy flux of this radiation at the sun is given by:
f=\frac{hc r^{3}n}{4d^{2}\lambda t}

Acetic acid  /əˈsiːtɪk/, systematically named  ethanoic acid  /ˌɛθəˈnoʊɪk/, is a colourless liquid  organic compound  with the  chemical formula  ch3cooh (also written as ch3co2h or c2h4o2). when undiluted, it is sometimes called  glacial acetic acid.  vinegar  is no less than 4% acetic acid by volume, making acetic acid the main component of vinegar apart from water. acetic acid has a distinctive sour taste and pungent smell. in addition to household vinegar, it is mainly produced as a precursor to  polyvinyl acetate  and  cellulose acetate. it is classified as a  weak acid  since it only partially  dissociates  in solution, but concentrated acetic acid is corrosive and can attack the skin.acetic acidnamespreferred iupac nameacetic acidsystematic iupac nameethanoic acidother namesvinegar (when dilute); hydrogen acetate; methanecarboxylic acid[1][2]identifierscas number64-19-7  3d model (jsmol)interactive image3dmetb00009 reference506007chebichebi: 15366  chemblchembl539  chemspider171  drugbankdb03166  echa infocard100.000.528ec number200-580-7e numbere260  (preservatives)gmelin reference1380iuphar/bps1058keggd00010  meshacetic+acidpubchem  cid176rtecs numberaf1225000uniiq40q9n063p  un number2789inchiinchi=1s/c2h4o2/c1-2(3)4/h1h3,(h,3,4)  key:   qtbsbxvteameqo-uhfffaoysa-n  smilescc(o)=o

Answerboth technicians (a) and (b);

Ithink the answer is c. make unnecessarily  wide gestures