Energy Sources in Stars (§10.3)

Can Fusion Occur in Sun’s s Core?Even with tunnelling, , are stars hot enough for nuclear reactions to proceed?λ = h/p is the wavelength associated with a massive particle (p = momentum)In terms momentum, the kinetic energy of a proton is:1/2 m p v 2 = p 2 /2m pAssuming proton must be within 1 de Broglie λ of its target to tunnelset distance, r, of closest approach to λ, (where barrier height = original K.E.incoming particle) gives:e 2 /r = e 2 /λ = p 2 /2m p = (h/λ) 2 /2m pSolving for λ (=h 2 /2m p e 2 ) and substituting r = λ into 3/2 kT = e 2 /r, we get theQM estimate of the temperature required for a nuclear reaction to occur:QM = 4/3(e 4 m p /kh 2 ) - putting in numbersT QMT QMQM = 10 7 K which is comparable to T core . Therefore, fusion is feasible atcentre of Sun