Comprehension Max Planck noted in 1899 the existence of a system of units based on the three fun...
0Comprehension
Max Planck noted in 1899 the existence of a system of units based on the three fundamental constants \( G, c \), and \( h \). These constants are dimensionally independent in the sense that no combination is dimensionless and a length, a time, and a mass may be constructed from them. Specifically, with \( \hbar \equiv \frac{h}{2 \pi}=1.05 \times 10^{-34} \) SI units in preference to \( h \), the Planck scale is represented by \( \ell_{P}, T_{P}, M_{P} \).
Which among the following would be the order of numerical value of a unit of mass defined in terms of \( \hbar, c \) and \( G \) ?
(a) \( 10^{-8} \mathrm{~kg} \)
(b) \( 10^{-10} \mathrm{~kg} \)
(c) \( 10^{-5} \mathrm{~kg} \)
(d) \( 10^{-27} \mathrm{~kg} \)
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