According to classical physics, $10^{-15}\ m$ is distance of closest approach $(d_c)$ for fusion to occur between two protons. A more accurate and quantum approach says that ${d_c} = \frac{{{\lambda _p}}}{{\sqrt 2 }}$ where $'\lambda _p'$ is de-broglie's wavelength of proton when they were far apart. Using quantum approach, find equation of temperature at centre of star. [Given: $M_p$ is mass of proton, $k$ is boltzman constant]

• A

  $\frac{{{e^4}{M_p}}}{{24{\pi ^2}\varepsilon _0^2k{h^2}}}$

• B

  $\frac{{{e^4}{M_p}}}{{12{\pi ^2}\varepsilon _0^2k{h^2}}}$

• C

  $\frac{{{e^2}{M_p}}}{{24{\pi ^2}\varepsilon _0^2k{h^2}}}$

• D

  $\frac{{{e^4}{M_p}}}{{6{\pi ^2}\varepsilon _0^2k{h^2}}}$