The characteristic distance at which quantum gravitational effect… - Vidyadip

MCQ

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?

A
$G^2hc$
✓
${\left( {\frac{{Gh}}{{{c^3}}}} \right)^{\frac{1}{2}}}$
C
${G^{\frac{1}{2}}}{h^2}c$
D
$Gh^2c^3$

✓

Answer

Correct option: B.

${\left( {\frac{{Gh}}{{{c^3}}}} \right)^{\frac{1}{2}}}$

b
Plank length is a unit of length

$I_p\,= 1.616229\times10^{-35}\,m$

${l_p} = \sqrt {\frac{{hG}}{{{c^3}}}} $

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