Make it easy to read please thanks! The purpose of this question is to explain w

Question

Make it easy to read please thanks!

The purpose of this question is to explain why diatomic molecules never rotate along their long axis at any reasonable temperature by thermal fluctuations. That this is forbidden by quantum mechanics. (a). Consider rotational motion. Write down the general definition of moment of inertia I. It has the dimension of (choose correct answer) [I] = kg m; [I] = kg m^2; [I] = kg m^2/sec; [I] = kg m/sec (b). Consider atomic hydrogen. Estimate the moment of inertia of the electron in its ground state, and compare this value with the moment of inertia of the nucleus treating the latter a solid ball with a uniform density distribution. In the following we assume that the electron cloud decouples from the nuclear core and does not participate in the rotations in case molecular hydrogen starts to spin along its long axis. (The energy levels of the two electrons are discrete and the energy gap between the ground state and the first excited state is much larger than k_B T at all reasonable temperatures.) (c). The effective radius in the moment of inertia for molecular hydrogen rotation of the type discussed in the previous problem is closest to (choose and explain the correct answer) Bohr radius; proton radius (d). The effective radius in the moment of inertia for molecular hydrogen rotation (spinning) along its long axis is closest to (choose and explain the correct answer) Bohr radius; proton radius (e). Estimate the ratio between the moments of inertia for molecular hydrogen in (c) and (d). (f). Estimate the temperature T_R where molecular hydrogen would start to spin along its long axis using your answer in (e). (See e.g., Fig. 1.13 in Schroeder.)

Explanation / Answer

(a) unit of moments of inertia=kg*m^2

(b)I=moment of inertia of electron=Mr^2 where M is mass of electron,r is ground state radius=0.0529 nm

I=2.54*10^(-51) kgm^2

for nucleus

I=0.4*M*r^2

r=1.75×1015 m

M=mass of 1 proton+mass of 1 neutron= 3.34432563 × 10-27 kg

I=4.09*10^(-57) kgm^2

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.