RMS Speed of Gas Molecules NEET Questions

Physics - Kinetic Theory of Gases

RMS Speed of Gas Molecules MCQ Questions


7.
The ratio of the most probable speed (vₘₚ), average speed (v̄), and RMS speed (vᵣₘₛ) is:
A.
vₘₚ : v̄ : vᵣₘₛ = 1 : 1.5 : 2
B.
vₘₚ : v̄ : vᵣₘₛ = 1 : 1 : 1
C.
vₘₚ : v̄ : vᵣₘₛ = √2 : √(8/π) : √3 ≈ 1 : 1.128 : 1.224
D.
vₘₚ : v̄ : vᵣₘₛ = 2 : 3 : 4
😑 View Answer Rough Work Error
ANSWER :
C. vₘₚ : v̄ : vᵣₘₛ = √2 : √(8/π) : √3 ≈ 1 : 1.128 : 1.224
8.
The most probable speed (vₘₚ) of gas molecules is defined as:
A.
The speed possessed by the maximum number of molecules — it corresponds to the peak of the Maxwell-Boltzmann speed distribution curve
B.
The arithmetic mean of all molecular speeds
C.
The square root of the mean of squares of speeds
D.
The speed at which the kinetic energy equals (3/2)RT
😑 View Answer Rough Work Error
ANSWER :
A. The speed possessed by the maximum number of molecules — it corresponds to the peak of the Maxwell-Boltzmann speed distribution curve
9.
The average speed (v̄) of gas molecules is given by:
A.
v̄ = √(8RT/πM) = √(8kBT/πm)
B.
v̄ = √(2RT/M)
C.
v̄ = √(3RT/M)
D.
v̄ = √(RT/M)
😑 View Answer Rough Work Error
ANSWER :
A. v̄ = √(8RT/πM) = √(8kBT/πm)
10.
The RMS speed of gas molecules is proportional to which power of absolute temperature?
A.
vᵣₘₛ ∝ T^(1/2) (proportional to the square root of absolute temperature)
B.
vᵣₘₛ ∝ T^(1/3)
C.
vᵣₘₛ ∝ T
D.
vᵣₘₛ ∝ T²
😑 View Answer Rough Work Error
ANSWER :
A. vᵣₘₛ ∝ T^(1/2) (proportional to the square root of absolute temperature)
11.
If the temperature of an ideal gas is increased from T₁ to T₂ = 4T₁, the RMS speed changes to:
A.
2vᵣₘₛ (the RMS speed doubles because vᵣₘₛ ∝ √T, and √(4T₁) = 2√T₁)
B.
vᵣₘₛ√2 (since the ratio is √(T₂/T₁) = √4 only partially)
C.
4vᵣₘₛ (since temperature is quadrupled)
D.
vᵣₘₛ/2 (since temperature ratio is inverted)
😑 View Answer Rough Work Error
ANSWER :
A. 2vᵣₘₛ (the RMS speed doubles because vᵣₘₛ ∝ √T, and √(4T₁) = 2√T₁)
12.
The temperature at which the RMS speed of a gas molecule is doubled compared to its value at 300 K is:
A.
600 K
B.
150 K
C.
900 K
D.
1200 K (since vᵣₘₛ ∝ √T; to double vᵣₘₛ, temperature must be quadrupled: 4 × 300 = 1200 K)
😑 View Answer Rough Work Error
ANSWER :
D. 1200 K (since vᵣₘₛ ∝ √T; to double vᵣₘₛ, temperature must be quadrupled: 4 × 300 = 1200 K)