Calculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.

Calculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom

Section: Chapter Questions

Problem 11.61E: What is the physical explanation of the difference between a particle having the 3-D rotational...

See similar textbooks

Related questions

Q: The nuclear spin of deuterium, D, is I= 1. Calculatethe ratio of the number of ways of achieving…

Q: The J = 0 to J = 1 rotational transition of the CO molecule occurs at a frequency of 1.15 x 1011…

A: To calculate the moment of inertia and bond length we first write down the given data: Transition=…

Q: Discuss the physical origins of the gross selection rules for microwave spectroscopy and rotational…

A: The gross selection rules give the knowledge about the allowed spectroscopic transitions. For…

Q: 5. Another unit that is used quite frequently in microwave spectroscopy is GHz (Gigahertz, 1x 10°…

Q: Why does the vibrational state of a diatomic molecule affect its rotational constant? Is there an…

A: Each vibrational level consists of several rotational levels. So the vibrational transition will…

Q: E11G.1(a) The line marked A in Fig. 11.5 is the fluorescence spectrum of benzophenone in solid…

A: Given: The fluorescence spectrum of benzophenone.

Q: Calculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.

Q: Rotational spectra are affected slightly by the fact that different isotopes have different masses.…

A: The reduced mass of a diatomic molecule is given by: The moment of inertia (I) is given by: where…

Q: The energy levels (in cm-1) of diatomic anharmonic oscillator are described by the following…

A: Introduction: Energy level in case of anharmonic oscillator is given as: Ev = (v+1/2)we-…

Q: (a) Calculate the moment of inertia of (i) 1H2, (ii) 2H2, (iii) 12C16O2, (iv) 13CO2 . (b) Calculate…

A: (a)

Q: For 'H3$Cl molecule, (N¡/No) ratio at 300 K is 6.091 x 10² . Calculate the wavenumber ( in cm') for…

Q: If the force constant of the C=N bond is 1.0 X103 N/m, calculate the vibrational frequency and…

A: Given: Force constant = 1.0 × 103 N/m.

Q: Consider the rotational spectrum of a linear molecule at 298 K with a moment of inertia of…

A: Introduction : We have to calculate the frequency and most populated state .

Q: What is the highest possible degeneracy of a vibration of a Cr(CO)6 molecule? Explain your answer.

A: To find: highest possible degeneracy of a vibration of a Cr(CO)6 molecule.

Q: Calculate the ratio A/B for transitions with the following characteristics: (i) 500 MHz…

A: i) The formula to calculate the ratio A/B for transition is given below. Where, A is the Einstein’s…

Q: What states of (i) benzene, (ii) naphthalene may be reached by electric dipole transitions from…

A: Refer to the character table for C3v Deducing a selection rule Is px→ py an allowed transition in a…

Q: A material has two energy levels with a separation of 2.1eV. At what temperature will the upper…

A: The ratio of the population of two energy state of an atom is given by N2N1=e-ΔEKT Where, N2 is the…

Q: 1. The general solution for a particle in a one-dimensional infinite potential well of width L is…

Q: Estimate the centrifugal distortion constant for 1H127I, for which ᷉ B = 6.511 cm−1 and ᷉v = 2308…

A: 1) B = 6.511 cm−1 2) v = 2308 cm−1 3) Substitution si done for 1H.

Q: What is the most highly populated rotational level of Cl2 at (i) 25 °C, (ii) 100 °C? Take ᷉ B =…

A: The most populated rotational energy level is given by, Jmax = (kT/2B)1/2 - 1/2 Note: 1 cm-1 = 12…

Q: 2/ Please explain the answer in detail The J = 0 to j = 1 transition for carbon monoxide (12C160)…

Q: The rotational constant for CO is 1.9314 cm−1 and 1.6116 cm−1 in the ground and first excited…

A: Given: Rotational constant for CO in the ground state, B=1.9314 cm−1 Rotational constant for CO in…

Q: Is the transition A1g → E2u forbidden for electric dipole transitions in a D6h molecule?

A: The selection rule for electric transition states that the transition between gerade (g) to ungerade…

Q: The NaH molecule undergoes a rotational transition from J=0 to J=1 when it absorbs a photon of…

Q: Develop an expression for the value of J corresponding to the most highly populated rotational…

A: An expression for the value of J corresponding to the most highly populated rotational energy level…

Q: assuming that the vibrations of a 35Cl2 molecule are equivalent to those of a harmonic oscillator…

A: The answer is given as follows

Q: The vibrational wavenumber of the oxygen molecule in its electronic ground state is 1580 cm−1,…

Q: Estimate the value of Erot for the lowest rotational energy state of N2, which has a bond length…

A: Rotation energy of any molecule is given by --- E = h28π2I where h is Planck's constant, I is the…

Q: The bond length of the C0O molecule is 112.8 pm. Calculate the following (a) The reduced mass. (b)…

A: The rotation of a molecule will be treated similarly to the rigid rotor. It will be similar to…

Q: Which of the three vibrations of an AB2 molecule are infrared or Raman active when it is (i)…

A: The vibrations on vibrational modes, which cause a change in permanent dipole moment of the molecule…

Q: The rotational constant of 1H35CI is 317.8 GHz. What is the separation of the lines in its pure…

A: Given data contains, The value of rotational constant (B) for 1H35CI is 317.8 GHz. (a) The…

Q: What is the energy separation between the n=4 and n=5 states for F2 molecule trapped within in one…

Q: In Raman, if we suppose a transition of (v=0-u=1), with selection rules of only (AJ=0 or ±2), this…

Q: Transitions in the rotational spectrum of the sodium chloride molecule, 23Na35CI, which is present…

A: The bond length of rigid rotor (diatomic molecule) can be determined using rotational spectroscopy

Q: The rotational Raman spectrum of 35Cl2 shows a series of Stokes lines separated by 0.9752 cm−1 and a…

A: Mass of a 35Cl atom is 34.9688 u. First calculate the reduced mass (μ) of 35Cl2 . Here m1 is the…

Q: Emission of microwave radiation from the J = 1 → 0 transition of a molecule has been detected at…

Q: For 'H³C1 molecule, (N¡/No) ratio at 300 K is 6.091 x 10² . Calculate the wavenumber ( in cm') for…

A: We know for rotational transition, EJ= BJ(J+1) cm-1 ; where B is rotational constant. From this…

Q: 7. The bond lengths of the symmetric top molecule CH3CI between C-H bond is 1.095 Å and C-Cl bond is…

A: For CH3Cl molecule, two different moment of inertia and thus, CHCl3 has two distinct rotational…

Q: A rotating methane molecule is described by the quantum numbers J, MJ, and K. (a) For methane, how…

A: (a)

Q: Explain the difference between the excitation and emission spectra of a molecule such as anthracene.

A: Emission spectrum An emissions spectrum can be defined as spectrum of the electromagnetic radiation…

Q: Calculate the energy of the J=0 to J=1 rotational transition of the O₂ molecule with a bond length…

A: Answer: To solve this question we have to use the relation between energy and rotational quantum…

Question

Calculate the energies of the first four rotational levels of ¹H¹²⁷I free to rotate in three dimensions; use for its moment of inertia I = μR², with μ = m_Hm_I/(m_H + m_I) and R = 160 pm. Use integer relative atomic masses for this estimate.

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

Using the rigid rotor model, calculate the energies in Joules of the first three rotational levels of HBr, using for its moment of inertia I = μR2, with μ = mHmX/(mH + mX) and equilibrium internuclear distance = 1.63 Å. To put these energies into units that make sense to us, convert energy to kJ/mol. (Simply estimate atomic masses from the average atomic weights of the elements given in the periodic table).
Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?
3. ^14N^16O (the superscripts represent the atomic mass number) (a) NO molecules rotate at an angular velocity of 2.01x10^12 rev/s, at the quantized rotational state with the rotational quantum number J of 3. Calculate the bond length of NO molecules. (b) Can NO molecules rotate under light irradiation? Explain your answer. (c) Calculate the effective force constant of the vibrational mode of NO at a frequency of 5.63x10^13 Hz measured by the infrared absorption spectrum. (d) NO has a bond energy of 6.29 eV. Applying the parabolic approximation to estimate the longest distance in which N and O atoms can be stretched before the dissociation of the molecular bond
An H2 molecule is in its vibrational and rotational ground states. It absorbs a photon of wavelength 2.211 2 μm and makes a transition to the υ = 1, J = 1 energy level. It then drops to the υ = 0, J = 2 energy level while emitting a photon of wavelength 2.405 4 mm. Calculate (a) the moment of inertia of the H2 molecule about an axis through its center of mass and perpendicular to the H–H bond, (b) the vibrational frequency of the H2 molecule, and (c) the equilibrium separation distance for this molecule.
4) Calculate the energies E of the first three rotational levels (those giving the minimal energy) of 1H35Cl molecule that is free to rotate in three dimensions. For its moment of inertia I = μeffR2 use the effective mass with μeff = mH * mCl / (mH + mCl) and bond length R = 127 pm.
(a) Calculate the moment of inertia of (i) 1H2, (ii) 2H2, (iii) 12C16O2, (iv) 13CO2 . (b) Calculate the corresponding rotational constants, expressing your answers as a frequency in hertz (Hz) and as a wavenumber in reciprocal centimetres (cm-1).
A diatomic molecule containing 35Cl and another atom has a rotational transition from J=0 to J=1 corresponding to a frequency of 7.70×109 Hz. The bond length is 267 pm. Use this information to calculate the reduced mass of the molecule, then find the atomic mass number of the other atom.
A space probe was designed to see 13CO in the atmosphere of Saturn by looking for lines in its rotational spectrum. If the bond length of CO is 112.8 pm, at what wave number do the first three rotational transitions appear?
Consider the rotational spectrum of a linear molecule at 298 K with a moment of inertia of 1.23×10−461.23\times10^{-46}1.23×10−46 kg m2 . (a) What is the frequency for the transition from J = 2 to J = 3? (b) What is the most populated rotational level for this molecule? Would the transition in (a) give the most intense signal in the rotational spectrum?
Calculate the vibrational energy of the v = 2 state of 1H127 I relative to the ground state, including the anharmonic corrections.
Which of the following transitions are electric-dipole allowed?(i) 1Σg+ ↔ 1Σu+, (ii) 3Σg+ ↔ 3Σu+, (iii) π* ↔ n.
The moment of inertia of CH4 can be ca lcu lated from the expression I= 8/3 MHR2 where R = 109 pm is the CH bond length. Ca lcu late the minimum rotational energy (other than zero) of the molecule and the degeneracy of that rotational state.