A gas consisting of diatomic molecules is at a temperature of 117 degr...
Rotational K.E = 2 ×Kb T/2. (as rotational degree of freedom f = 2. for diatomic molecules) & rotational K.E for axis passing through the center is K.E= 2 ×I w^2/2. .... equating both equation we get Kb T= Iw^2.. since, rms angular speed w= sqrt. Kb T/ I. after putting value we get option 4.
A gas consisting of diatomic molecules is at a temperature of 117 degr...
To find the rms (root mean square) angular speed of each molecule, we can use the formula:
ω = √(3kT / I)
where:
ω is the rms angular speed
k is the Boltzmann constant (1.38×10^-23 J/K)
T is the temperature in Kelvin
I is the moment of inertia of each molecule
Given:
Temperature, T = 117 degrees Celsius = 117 + 273 = 390 K
Moment of inertia, I = 1.5 × 10^-40 kgm^2
Boltzmann constant, k = 1.38×10^-23 J/K
Now, let's calculate the rms angular speed using the formula.
1. Convert the temperature to Kelvin:
T = 390 K
2. Plug in the values into the formula:
ω = √(3 * 1.38×10^-23 J/K * 390 K / 1.5 × 10^-40 kgm^2)
3. Simplify the equation:
ω = √(3 * 1.38×10^-23 J/K * 390 K / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×10^-23 J * 390 / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×10^-23 J * 390 / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×10^-23 J * 390 / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×10^-23 J * 390 / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×10^-23 J * 390 / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×10^-23 J * 390 / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×10^-23 J * 390 / 1.5 × 10^-40 kgm^2)
= √(3 * 1.38×390 / 1.5 × 10^17)
= √(3 * 537.3 / 1.5 × 10^17)
= √(1611.9 / 1.5 × 10^17)
= √(0.0108 × 10^17)
= √(1.08 × 10^15)
= 3.29 × 10^7 rad/s
Therefore, the rms angular speed of each molecule is approximately 3.29 × 10^7 rad/s, which is not one of the given answer options. It seems there might be an error in the given options or the calculation.
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.