What is Planck's constant dimensionally equal to?

Question

What is Planck's constant dimensionally equal to?

1 Answer

Impact of this question

7186 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-10-04T01:05:27

The dimensions of Planck's constant are $M L^{2} T^{- 1}$ $ML^2T^-1$ .

$E = h f$ $E = hf$ , so

$h = \frac{E}{f}$ $h = E/f$

$E = energy = force \times distance = mass \times acceleration \times distance$ $E = "energy" = "force × distance" = "mass × acceleration × distance"$

So $[E] = M \times L T^{- 2} \times L = M L^{2} T^{- 2}$ $[E] = M × LT^-2 × L = ML^2T^-2$ , where the brackets mean "units of".

$f = frequency$ $f = "frequency"$ , so $[f] = T^{- 1}$ $[f] = T^-1$

Then $[h] = \frac{M L^{2} T^{- 2}}{T^{- 1}} = M L^{2} T^{- 1}$ $[h] = (ML^2T^-2)/ T^-1 = ML^2T^-1$ .

In SI base units, $[h] = {kg\cdotm}^{2} s^{- 1}$ $[h] = "kg·m"^2"s"^-1$ .

In SI derived units, $[h] = J\cdots$ $[h] = "J·s"$ .

Science

Math

Humanities

... and beyond

What is Planck's constant dimensionally equal to?

1 Answer

Related questions

Impact of this question