Chapter 1: Problem 52
Radiation from a cesium-133 atom completes \(9,192,631,770\) cycles each second. How long does it take for this radiation to complete \(1.5\) million cycles?
Short Answer
Expert verified
It takes about 0.000163 seconds.
Step by step solution
01
Define the Rate of Cycles
The radiation from a cesium-133 atom completes \(9,192,631,770\) cycles per second. This rate will be used to find out how much time it takes for the radiation to complete a different number of cycles.
02
Set Up the Equation
To find the time taken to complete 1.5 million cycles, set up the equation based on the relationship: \( \text{Time} = \frac{\text{Number of cycles}}{\text{Cycles per second}} \).
03
Calculate the Time
Substitute the given values into the equation: \( \text{Time} = \frac{1,500,000}{9,192,631,770} \).
04
Compute the Result
Perform the division: \( \text{Time} \approx \frac{1,500,000}{9,192,631,770} \approx 0.000163205\) seconds.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Cesium-133 Atom
The cesium-133 atom is fundamental in the field of timekeeping. It is the atom used in atomic clocks, which are the most accurate timekeeping devices available today. Atomic clocks work on the principle that cesium-133 atoms vibrate at a very consistent frequency. These vibrations form the basis for the second, the basic unit of time in the International System of Units (SI). The reason cesium-133 is preferred is because of its stable frequency emission, making it perfect for precise measurements. These clocks can help in various applications, from GPS technology to scientific research where accurate time measurement is essential.
Time Calculation
Time calculation is crucial in understanding how many events occur over a given period. In the context of the original exercise, it involves determining how long it takes for a specified number of atomic cycles to complete. To calculate time, the relationship between the number of cycles and their frequency is vital. The formula used is:
- Time = \(\frac{\text{Number of cycles}}{\text{Cycles per second}}\)
Cycle Rate
The cycle rate refers to how often a repeating event occurs and is usually measured in cycles per second, known as Hertz (Hz). In the context of cesium-133, the cycle rate is essential in defining the atom's vibrational frequency. This frequency is used to measure time with high precision and is defined as \(9,192,631,770\) Hertz for cesium-133. A higher cycle rate indicates that events occur more frequently in a given period. Understanding the cycle rate can help in numerous scientific and practical tasks, such as assessing time intervals or syncing activities to a precise temporal schedule.
Physics Problem Solving
Physics problem-solving is about applying known physical principles to find unknown quantities. In problems like calculating time from a given cycle rate, the process involves setting up a clear mathematical model and using equations correctly. The solution is derived by understanding the relationship between the different components, such as number of cycles and cycle rate, which are given in the form of data.
- Identify the Known and Unknowns: Understand what information is provided and what needs to be solved.
- Apply Relevant Formulas: Use appropriate mathematical relations, like cycle formulas, to link knowns to unknowns.
- Perform Calculations: Substitute values into the formula and carry out arithmetic operations.