USAAAO — 2022 First Round

A star with mass M goes through an energy-generating nuclear reaction 4 ¹H → ⁴He + Energy. Here, the burning efficiency of the p-p (proton-proton) chain is 0.007, meaning that each mass m yields 0.007mc² of energy. Assuming the total available hydrogen mass for nuclear reaction amounts to half of its original mass, and the luminosity L stays constant throughout the burning phase, give an expression of the hydrogen-burning lifetime of the star.