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###### 19PHB104 Quantum Mechanics

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###### OSCI16 General Physics

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Type

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## Question:

### Description

The second was defined in 1967 using the hyperfine splitting of the ground state of cesium, which, at //kips = 9 192 631 770 Hz, is in the microwave region of the electromag-netic spectrum. This was chosen in part for technical reasons, as it was then possible to couple a microwave cavity to an external oscillator to build a clock. However, the fractional instability of an atomic clock is given by the Allan deviation, ay(T) Au vos,ifir where vo is the transition frequency, Av the width of the transition, N the number of atoms involved, and r the interrogation time. It is clear that a more stable clock can be achieved by using a higher transition frequency.

While there are still technical challenges to building a very-high precision atomic clock using an optical transition, research is progressing and the second might have to be redefined in the near future. One potential candidate is what is called an optical lattice clock based on strontium atoms.

1. The first 9 energy levels corresponding to the ground, first excited, and second excited electronic configurations of Sr have the following energy and total angular momentum:

2. (a) Give the full designation, i.e., ni of each level and draw an energy diagram (to scale) with all the levels in the correct order. Discuss the validity of the Russell-Saunders coupling scheme and the Londe interval rule as it applies to Sr. (c) For the first three levels of the first excited electronic configuration, show how each ILSJ Alr) state is constructed from non-spin-orbit-coupled states using Clebsch-Gordan coefficients.

(b) The proposed transition for a 'Sr lattice clock was measured as 429 228 004 229 952 Hz, with an uncertainty of ±15 Hz. What are the levels involved in this transition? Discuss the transition from the point of view of selection rules.
3. By how much does the transition in question 2 change when substituting 88Sr (m = 87.905 619 u) for "Sr (m = 86.908 884 u)?

4. The Earth's magnetic field is about 5 x ars T. By how much does this affect the transition of the strontium clock?

5. The ionization energy of Sr is 5.694 85eV. Compare to hydrogen and helium and discuss.

### ED2235 Atomic Physics for Fusion 6.0 credits

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## More ED2235 Atomic Physics for Fusion 6.0 credits: Questions & Answers

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Q

### 19PHB104 Quantum Mechanics

Questions: Learning outcomesThis coursework assesses your ability to1. analyse the results of a computer simulation of an experiment.2. solve problems by using the appropriate mathematical techniques.3. describe quantum states of discrete systems and discuss the interpretation of quantum mechanic ...

Q

### OSCI16 General Physics

Questions: 1) A family is building a tyre swing for their children. The tyre is hung from a fairly level branch by two ropes which come down and are tied around the tyre at one point which makes the top of the swng. The left rope has an angle of 68° from the horizontal branch and when a 31 kg ch ...

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