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, ℏ and c. Which of the following correctly gives the Planck length?

Question

Accepted Answer

(3) ((Gℏ)/(c³))^1/2. Given: G=[M⁻¹L³T⁻²], ℏ=[ML²T⁻¹], c=[LT⁻¹]. Gℏ=[L⁵T⁻³], the mass having cancelled. (Gℏ)/(c³)=([L⁵T⁻³])/([L³T⁻³])=[L²]. Taking the square root gives a length, so the Planck length is ((Gℏ)/(c³))^1/2.

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, ℏ and c. Which of the following correctly gives the Planck length?

Step-by-step solution

Why the other options are wrong