Hello, everyone today we will discuss a few **questions with solutions under the quantum chemistry** in the rigid rotator chapter. Correspond to examine molecular spectroscopy, Rotational spectroscopy (or Microwave Spectroscopy), Rotational constant (B), Moment of inertia (I), Reduced mass, etc.

we have to discuss the concept of quantum spectroscopy freely. Basic Knowledge or concept of rotational spectroscopy.

### Principle of Rotational Spectroscopy:

In the rotational or microwave spectroscopy two energy lines (two transitional lines) distance is 2B. Where B is the rotational constant.

A rigid rotator undergoes transitions from one energy to another energy level. The allowed transitions state is ∆𝑙=∓1, that is the selection rule.

we have to consider the absorption of electromagnetic radiation, the molecule transition from quantum number l to l+1. The energy difference then is given below.

Energy difference quantum number l to l+1 see in equation no. (i)

Using the Bohr frequency, compered the equation (i) and (ii) then we get the value of 𝜈,

Bohr Frequency 𝜈={ℎ/(4𝜋^{2} 𝐼)}(𝑙+1). Where 𝑙=0, 1, 2, 3…..

We know that the Microwave spectroscopy frequency is 𝜈=2𝐵(𝑙+1). Where 𝑙=0, 1, 2, 3…..

we get the rotational constant 𝐵=ℎ/(8𝜋^2 𝐼). Where I= Moment of Inertia = (Reduced mass) × (Distance)^{2} =𝜇r^{2}

### Solve the problem of Quantum chemistry (Spectroscopy):

Now, solve the problem under microwave spectroscopy very easily if those basic principles are known. This suggestive question with a solution for CSIR UGC NET, GATE, and IIT JAM and correspond to other national level entrance exams. As an aspirant, this chapter of Quantum chemistry (spectroscopy -Rotational) read and solves this question.

#### Q.2. To a good approximation, the microwave spectrum of H^{35}Cl consists of a series of equally spaced lines, separated by 6.26 × 10^{11} Hz. Calculate the bond length of H^{35}Cl.

Option:

(A) 2.29 × 10^{-10} m (B) 2.29 × 10^{-8} m

(C) 1.29 × 10^{-10} m (D) 1.29 × 10^{-8} m

**Answer:**

Option: (C) 1.29 × 10^{-10} m. Quantum chemistry question number two right answer is 1.29 × 10^{-10} m.

**Hints:**

We can see that the given question finds out the bond length of the diatomic molecule H^{35}Cl. First of all, we know that **the spacing of the lines in the microwave spectrum of H ^{35}Cl is 2B**. Where B is the Rotational constant. The formula of the Rotational constant is

𝐵=ℎ/(8𝜋^2 𝐼) ……….(i)

Where I= Moment of Inertia = (Reduced mass) × (Distance)^{2} =𝜇r^{2} ………..(ii)

In case r is the Bond length of the given diatomic molecule H35Cl and 𝜇 is Reduced the mass of this diatomic molecule.

Reduced mass 𝜇 = (m_{H}.m_{Cl})/(m_{H} + m_{Cl}) = (1 × 35)/(1+36) =35/36 =0.973 amu = 0.973 × 1.67 ×10^{-27} Kg.

𝜇 =1.62 × 10^{-27} Kg. Where 1amu = 1.67 ×10^{-27} Kg.

Now, **the spacing of the lines in the microwave spectrum of H ^{35}Cl is 2B** = 6.26 × 10

^{11}Hz.

Put the value of 2B and Plank Constant h = 6.626 × 10^{-34} J.s in equation (i) we get the Moment of inertia I= 2.68 × 10^{-47} Kg. m^{2}.

Finally, put the value of reduced mass 𝜇 =1.62 × 10^{-27} Kg and moment of inertia I= 2.68 × 10^{-47} Kg. m^{2} on equation (ii) we get the Bond length of H^{35}Cl equal to 1.29 × 10^{-10} m.

#### Image solution:

### Reference:

Few most popular and common books for Quantum chemistry. Read out the basic principle of quantum chemistry on spectroscopy below suggestion:

- The best book for quantum chemistry is
**Donald A McQuarrie Viva’s student edition Quantum Chemistry**. These are quality and quantitive books for chemistry students. -
**Quantum Chemistry Book by Ira N. Levine**. It is a good rating book any time. **Molecular Quantum Mechanics Book by Peter Atkins**. This book for basic knowledge of quantum chemistry postulates and concept of box particle.

### Quantum-chemistry questions and answers pdf:

We have to provide quantum chemistry questions and answers pdf free to download. The PDF of the Basic principle of molecular spectroscopy (Quantum chemistry -spectroscopy). Click on the PDF file and free to download it.

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