question_answer

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants \[G,h\] and\[c\]. Which of the following correctly gives the Planck length? [JEE Online 15-04-2018 (II)]

A) \[{{G}^{2}}hc\]

B) \[{{\left( \frac{Gh}{{{c}^{3}}} \right)}^{\frac{1}{2}}}\]

C) \[{{G}^{\frac{1}{2}}}{{h}^{2}}c\]

D) \[G{{h}^{2}}{{c}^{3}}\]