Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
Question
Chapter 16, Problem 16.8E
Interpretation Introduction

(a)

Interpretation:

The values of ΔE in the transition energies for each individual transition for the 1S1P transition when a sample is exposed to a magnetic field of 2.35 T are to be calculated.

Concept introduction:

The phenomenon of splitting of a spectral line when a magnetic field is applied to it is known as Zeeman Effect. Magnetic field strength can be measured by using the Zeeman Effect. Applications of Zeeman Effect include NMR spectroscopy, MRI and electron spin resonance spectroscopy.

During an electronic transition, an electron from ground state moves straight to the excited state keeping the internuclear distance constant.

The change in the energy of the state, ΔE is calculated by the formula shown below.

ΔE=μBMLB

Expert Solution
Check Mark

Answer to Problem 16.8E

The values of ΔE in the transition energies for 1P in the 1S1P transition are 2.18×1023 J, 0 J and +2.18×1023 J.

Explanation of Solution

In case of 1S1P transition, the splitting of 1S state does not take place because for this state, the value of L=0 and so ML=0. Therefore, splitting of only 1P state occurs due to the presence of degenerate ML=10 and +1 states. The value of ΔE is calculated by the formula shown below.

ΔE=μBMLB…(1)

Where,

μB is the Bohr magneton (9.274×1024J/T).

ML is the magnetic quantum number.

B is the magnetic field.

The value of magnetic field is 2.35 T.

For, ML=1.

Substitute the values of μB, B and ML=1 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×1×2.35 T=2.179×1023 J2.18×1023 J

For, ML=0

Substitute the values of μB, B and ML=0 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×0×2.35 T=0 J

For, ML=+1.

Substitute the values of μB, B and ML=+1 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×+1×2.35 T=+2.179×1023 J+2.18×1023 J

Therefore, the values of ΔE in the transition energies for 1P in the 1S1P transition are 2.18×1023 J, 0 J and +2.18×1023 J.

Conclusion

The values of ΔE in the transition energies for 1P in the 1S1P transition are 2.18×1023 J, 0 J and +2.18×1023 J.

Interpretation Introduction

(b)

Interpretation:

The values of ΔE in the transition energies for each individual transition for the 1P1D transition when a sample is exposed to a magnetic field of 2.35 T are to be calculated.

Concept introduction:

The phenomenon of splitting of a spectral line when a magnetic field is applied to it is known as Zeeman Effect. Magnetic field strength can be measured by using the Zeeman Effect. Applications of Zeeman Effect include NMR spectroscopy, MRI and electron spin resonance spectroscopy.

During an electronic transition, an electron from ground state moves straight to the excited state keeping the internuclear distance constant.

The change in the energy of the state, ΔE is calculated by the formula shown below.

ΔE=μBMLB

Expert Solution
Check Mark

Answer to Problem 16.8E

The values of ΔE in the transition energies for 1P in 1P1D transition are 2.18×1023 J, 0 J and +2.18×1023 J.

The values of ΔE in the transition energies for 1D in 1P1D transition are 4.358×1023 J, 2.18×1023 J, 0 J, +2.18×1023 J and +4.35×1023 J.

Explanation of Solution

In case of 1P1D transition, the splitting of 1P state occurs due to the presence of degenerate ML=10 and +1 states. The value of ΔE is calculated by the formula shown below.

ΔE=μBMLB…(1)

Where,

μB is the Bohr magneton (9.274×1024J/T).

ML is the magnetic quantum number.

B is the magnetic field.

The value of magnetic field is 2.35 T.

For, ML=1.

Substitute the values of μB, B and ML=1 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×1×2.35 T=2.179×1023 J2.18×1023 J

For, ML=0

Substitute the values of μB, B and ML=0 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×0×2.35 T=0 J

For, ML=+1.

Substitute the values of μB, B and ML=+1 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×+1×2.35 T=+2.179×1023 J+2.18×1023 J

Therefore, the values of ΔE in the transition energies for 1P are 2.18×1023 J, 0 J and +2.18×1023 J.

In case of 1P1D transition, the splitting of 1D state occurs due to the presence of degenerate ML=210+1 and +2 states. The value of ΔE is calculated by the formula shown below.

ΔE=μBMLB…(1)

Where,

μB is the Bohr magneton (9.274×1024J/T).

ML is the magnetic quantum number.

B is the magnetic field.

The value of magnetic field is 2.35 T.

For, ML=2.

Substitute the values of μB, B and ML=2 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×2×2.35 T=4.358×1023 J

For, ML=1.

Substitute the values of μB, B and ML=1 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×1×2.35 T=2.179×1023 J2.18×1023 J

For, ML=0

Substitute the values of μB, B and ML=0 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×0×2.35 T=0 J

For, ML=+1.

Substitute the values of μB, B and ML=+1 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×+1×2.35 T=+2.179×1023 J+2.18×1023 J

For, ML=+2.

Substitute the values of μB, B and ML=+2 in equation (1) to calculate the change in energy.

ΔE=9.274×1024J/T×+2×2.35 T=+4.35×1023 J

Therefore, the values of ΔE in the transition energies for 1D are 4.358×1023 J, 2.18×1023 J, 0 J, +2.18×1023 J and +4.35×1023 J.

Conclusion

The values of ΔE in the transition energies for 1P in 1P1D transition are 2.18×1023 J, 0 J and +2.18×1023 J.

The values of ΔE in the transition energies for 1D in 1P1D transition are 4.358×1023 J, 2.18×1023 J, 0 J, +2.18×1023 J and +4.35×1023 J.

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