It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to (4/π)×1011 Hz. Then the moment of inertia of CO molecule about its centre of mass is close to (Take h = 2π×10-34 J -s)

Question

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to (4/π)×1011 Hz. Then the moment of inertia of CO molecule about its centre of mass is close to (Take h = 2π×10-34 J -s) (A) 2.76×10-46 kg-m2 (B) 1.87×10-46 kg-m2 (C) 4.67×10-47 kg-m2 (D) 1.17×10-47 kg-m2

Tardigrade Admin · Accepted Answer

hv=K2-K1=(3h2/8π2I) ∴ I=(3h/8π2f)=(3×2π×10-34×π/8×π2×4×1011) =1.87×10-46kg-m2 ∴ The correct answer is (b).

Q. It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to $\frac{4}{π} \times 1 0^{11}$ Hz. Then the moment of inertia of CO molecule about its centre of mass is close to (Take $h = 2 π \times 1 0^{- 34}$ J -s)

$2.76 \times 1 0^{- 46} k g - m^{2}$

$1.87 \times 1 0^{- 46} k g - m^{2}$

$4.67 \times 1 0^{- 47} k g - m^{2}$

$1.17 \times 1 0^{- 47} k g - m^{2}$

$h v = K_{2} - K_{1} = \frac{3 h ^{2}}{8 π ^{2} I}$
$∴ I = \frac{3 h}{8 π ^{2} f} = \frac{3 \times 2 π \times 1 0 ^{- 34} \times π}{8 \times π ^{2} \times 4 \times 1 0 ^{11}}$
$= 1.87 \times 1 0^{- 46} k g - m^{2}$
$∴$ The correct answer is (b).

Q. It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to π4​×1011 Hz. Then the moment of inertia of CO molecule about its centre of mass is close to (Take h=2π×10−34 J -s)

2.76×10−46kg−m2

1.87×10−46kg−m2

4.67×10−47kg−m2

1.17×10−47kg−m2