THANK YOU!!
What is a combination of h (plancks constant), c(speed of light) and G (6.67x10^-11 Nm^2 / kg^2)
that has units of length?
You're welcome! To find a combination of Planck's constant (h), the speed of light (c), and the gravitational constant (G), that has units of length, we need to analyze the units of these constants and find a suitable combination.
1. Planck's constant (h) has units of energy multiplied by time, or J·s.
2. The speed of light (c) has units of distance divided by time, or m/s.
3. The gravitational constant (G) has units of force multiplied by distance squared and divided by mass squared, or N·m^2/kg^2.
Since we need a combination of these constants that has units of length, we can start by considering dimensional analysis and trying to cancel out units.
One approach is to divide Planck's constant (h) by the product of the speed of light (c) and the gravitational constant (G). Let's perform the calculation:
[h / (cG)] = [(J·s) / (m/s) · (N·m^2/kg^2)]
To simplify this expression, we can rearrange the units, cancel out like terms, and simplify:
[h / (cG)] = [(J·s) / (m/s) · (N·m^2/kg^2)]
= [(J·s) / (m/s) · (N·m^2/kg^2)]
= [(J · m) / (m · s) · (N · m^2 / kg^2)]
= [(N · m^2·s) / (m·m·kg^2·s)]
= [(N·m) / kg]
Therefore, the combination of h, c, and G that has units of length is [(N·m) / kg].