The dimensional formula of Planck's constant h is [M L^2 T^-1]. You get it from E = h*nu, so h = E / nu = (energy) / (frequency) = [M L^2 T^-2] / [T^-1] = [M L^2 T^-1]. Memory hook: h has the SAME dimensions as angular momentum (L = m*v*r), because both are "energy multiplied by time" (action).
Planck's constant h = E / nu. Dividing energy [M L^2 T^-2] by frequency [T^-1] gives h = [M L^2 T^-1], the same dimensions as angular momentum. SI unit: joule second (J s).
Your doubts, answered
How do I derive the dimensions of Planck's constant from E = h*nu?
Start from the Planck relation E = h*nu, where E is energy and nu (frequency) has unit hertz. Rearrange to h = E / nu. Energy has dimensions [M L^2 T^-2] and frequency has dimensions [T^-1] (one over time). So h = [M L^2 T^-2] / [T^-1] = [M L^2 T^-2] * [T^+1] = [M L^2 T^-1]. That is the answer for NEET: [M L^2 T^-1].
Why does Planck's constant have the same dimensions as angular momentum?
Angular momentum L = m*v*r = [M][L T^-1][L] = [M L^2 T^-1]. Planck's constant is also [M L^2 T^-1]. Both are examples of 'action' in physics (energy multiplied by time). This is why h appears in the quantum condition m*v*r = n*h/(2*pi) for Bohr orbits. In NEET, if a question asks 'which quantity has the same dimensions as h', the answer is angular momentum.
Is Planck's constant dimensionless like a pure number?
No. Planck's constant is NOT dimensionless. It has real dimensions [M L^2 T^-1] and the SI unit joule-second (J s). Only ratios like refractive index or strain are dimensionless. Do not confuse h with dimensionless constants; that mistake loses easy marks.
What is the SI unit of Planck's constant?
The SI unit of h is joule second (J s), because h = E / nu = joule / (1/second) = joule*second. Its value is about 6.626 x 10^-34 J s. Unit J s matches the dimensions [M L^2 T^-1], since joule = kg m^2 s^-2 and multiplying by second gives kg m^2 s^-1.
⚠️ The NEET trap ✗ Writing h = E * nu, giving dimensions [M L^2 T^-3]. ✓ h = E / nu (divide energy by frequency), giving [M L^2 T^-1]. 🧠 E = h*nu means h = E/nu, NOT E*nu. Frequency is [T^-1], so dividing by it ADDS one power of T: energy [M L^2 T^-2] becomes h [M L^2 T^-1].
Real NEET questions
NEET 2016
Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
A · sqrt(hG/c^3) ✓
B · sqrt(hG/c^5)
C · sqrt(hc/G)
D · sqrt(Gc/h^3)
Solution: Write length as L = h^a * c^b * G^c. Use dimensions: [h] = [M L^2 T^-1], [c] = [L T^-1], [G] = [M^-1 L^3 T^-2]. Now match powers of M, L, T on both sides for [L] = [M^0 L^1 T^0].\nM: a - c = 0\nL: 2a + b + 3c = 1\nT: -a - b - 2c = 0\nFrom M: a = c. Add the L and T equations: (2a+b+3c) + (-a-b-2c) = 1 + 0, so a + c = 1. With a = c, this gives a = c = 1/2. Put back into T equation: -1/2 - b - 1 = 0, so b = -3/2.\nTherefore length = h^(1/2) * c^(-3/2) * G^(1/2) = sqrt(hG / c^3). Correct option is A.
Solved Units And Measurements NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the dimensional formula of Planck's constant?
[M L^2 T^-1]. It is found from h = E / nu = energy / frequency = [M L^2 T^-2] / [T^-1] = [M L^2 T^-1].
Planck's constant has the same dimensions as which physical quantity?
Angular momentum (m*v*r) and also the quantity 'action' (energy multiplied by time). All three are [M L^2 T^-1]. This is a common NEET matching question.
What is the SI unit of Planck's constant?
Joule second (J s). Its value is about 6.626 x 10^-34 J s.
Does h have the dimensions of energy?
No. Energy is [M L^2 T^-2]. Planck's constant is [M L^2 T^-1], which is energy divided by frequency (energy multiplied by time).
Why is Planck's constant important for NEET dimensional questions?
h combines with c and G to form the Planck length, and it matches angular momentum in dimensions. NEET often asks you to build length, mass or time from h, c, G, so knowing [h] = [M L^2 T^-1] is essential.
