In interstellar space, atomic hydrogen produces the sharp spectral line called t

Question

In interstellar space, atomic hydrogen produces the sharp spectral line called the 21 cm radiation, which astronomers find useful in detecting clouds of hydrogen between stars since dust, which can block visible light, is transparent to radio waves. This 21.11 cm radiation to be more precise is the result of a spin-flip transition when the spins of the electron and proton in the nucleus are either aligned or counter-aligned. Explain your reasoning for the key steps that allow you to determine: (a) which condition of the spins has the higher energy; (b) the energy difference between these two spin states; (c) the life-time of the upper state if the width of this spectral line is observed to be 1.04x10–30 eV.

Explanation / Answer

a ) The state in which the electron and protons spins are parallel is slightly higher in the energy than in the state in which they are antiparallel b ) the energy difference between these two spin states is      E = 1240 n m e V / 21.11*10^-2 m             = 1240*10^-9 m eV / 21.11*10^-2 m             = 1240 m eV / 21.11*10^-2 * 10^9 m             = 58.74 *10^-7 eV c ) the life-time of the upper state if the width of this spectral line is observed to be 1.04x10–30 eV.        From the uncertainity relation        E t = h / 4          t = h / 4 * E                  = 6.625 *10^-34 J s / 4 * 1.04x10–30 eV.                  = 6.625 *10^-34 J s / 4 * 1.04x10–30 * 1.6*10^-19 J                 = 3.16*10^14 s                 = 1.00*10^7 years

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