The de-Broglie wavelength associated with a particle of mass m and energy E is h/√(2mE). The dimensional formula for Planck's constant is: (a) [M²L²T⁻²] (b) [ML⁻¹T⁻²] (c) [ML²T⁻¹] (d) [MLT⁻²]

Answer: (c). λ = h/√(2mE) ⇒ h = λ√(2mE). √(mE) is momentum: [MLT⁻¹]. [h] = [L][MLT⁻¹] = [ML²T⁻¹]. So the answer is (c).

The de-Broglie wavelength associated with a particle of mass m and… | JEE Main 2024 (9 Apr, Shift 2)

Q18JEE Main 2024 · 9 APR · SHIFT 2Easy

Applications of Dimensional Analysis

The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h/\sqrt{2mE}$ . The dimensional formula for Planck's constant is:

Show answer and solution

Answer: (c)

What is the dimensional formula of ab⁻¹ in the equation (P + a/V²)(V - b) = RT, where…JEE Main 2024 (5 Apr, Shift 2)
Applying the principle of homogeneity of dimensions, determine which one is correct…JEE Main 2024 (4 Apr, Shift 2)
The equation of stationary wave is: y = 2asin ((2)/(λ))cos ((2π x)/(λ)). Which of the…JEE Main 2024 (4 Apr, Shift 1)
Consider two physical quantities A and B related to each other as E = (B - x²)/(At) where…JEE Main 2024 (31 Jan, Shift 2)
A force is represented by F = ax² + bt1/2 where x = distance and t = time. The dimensions…JEE Main 2024 (31 Jan, Shift 1)
If mass is written as m = kcPG-1/2h1/2 then the value of P will be: (Constants have their…JEE Main 2024 (30 Jan, Shift 2)
The equation of state of a real gas is given by (P + a/V²)(V - b) = RT, where P, V and T…JEE Main 2024 (27 Jan, Shift 2)
In the equation [X + a/Y²][Y - b] = RT, X is pressure, Y is volume, R is universal gas…JEE Main 2023 (13 Apr, Shift 2)