Question

The dimensional formula of Planck’s constant is

• A. [ML²T^-3]
• B. [ML²T⁰]
• C. [ML²T^-1]
• D. [M⁰L⁰T⁰]

Hint:

Remember the equation \( E = h \nu \) to deduce the dimensional formula of Planck’s constant. Use known dimensional formulas: Energy: [ML\textsuperscript{2}T\textsuperscript{-2}] Frequency: [T\textsuperscript{-1}] Divide energy’s dimension by frequency’s to get that of \( h \).

Answer 1

The Correct Option is C

Step 1: Recall the definition of Planck’s constant.
Planck's constant \( h \) appears in the relation \( E = h \nu \), where \( E \) is energy and \( \nu \) is frequency. 
Step 2: Use dimensional formulas.
Energy: [ML²T^-2]
Frequency: [T^-1]
Step 3: Derive the dimensional formula of \( h \).
Since \( h = \frac{E}{\nu} \), we have:
\[ [h] = \frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}] \] So the dimensional formula of Planck’s constant is: [ML²T^-1] 
Step 4: Select the correct option.
The derived dimensional formula [ML²T^-1] matches option (3).