Question

In the relation P = (α Z)/(β) e⁻ᵏθ, P is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be:

• A. [M⁰L²T⁰]
• B. [ML²T⁻¹]
• C. [ML⁰T⁻¹]
• D. [M⁰L²T⁻¹]

Hint:

Exponential and trigonometric terms are always dimensionless.

Answer 1

The Correct Option is B

Step 1: Dimension of pressure, [P] = [ML⁻¹T⁻²]
Step 2: Since exponential terms are dimensionless, [P] = ([α][Z])/([β])
Step 3: Taking [α]=[ML⁻¹T⁻²] and [Z]=[L], [β] = [ML²T⁻¹]