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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 ?
- G²hc
- (Gh/c³)^(1/2)
- G^(1/2)h²c
- Gh²c³
Correct answer: (Gh/c³)^(1/2)
Solution
The Planck length is the unique combination of G, h, c with dimension of length: l_P = sqrt(Gh/c^3) (approx 1.6e-35 m). So option (Gh/c^3)^(1/2) is correct.
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