Question

plank's constant has the dimensions. answer_ energy​

Answer 1

Answer:

Hint: Planck's constant appears in the equation of energy of a photon and the equation of De Broglie wavelength. The dimension of energy is ML2T−2. The dimension of frequency is T−1 and of angular momentum is ML2T−1. Dimensions of mass, distance and time are M,Land Trespectively.

Formula used: Energy of a photon, E=hν, where h is the Planck's constant and ν is the frequency of the photon.

De Broglie Wavelength, λ=hp, where p is the momentum.

Complete step by step answer:

The energy of a photon of radiation is given by E=hν

Now, we can do the dimensional analysis on energy and frequency

[E]=[h][ν]

So, we must substitute the values of dimensions of energy and frequency from the hint

ML2T−2=[h]T−1

⇒[h]=ML2T−2T−1⇒[h]=ML2T−1…(1)

Now, velocity is distance divided by time. This gives dimensions of velocity,

v=LT−1

Also, momentum is mass multiplied by velocity,

This gives dimensions of momentum,

[p]=MLT−1

Furthermore, angular momentum has the same units as linear momentum multiplied with distance. So, we can find the dimensions of angular momentum.

[l]=ML2T−1…(2)

Equating equations (1) and (2) we get,

[h]=[l]

Hence, the dimensions of Planck's constant are equal with the dimensions of angular momentum.

Answer 2

ENERGY...

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