Chapter 12: Problem 20
Look up the diameter of a silicon atom, in \(\AA\). The channel length in a Pentium 4 processor chip is \(65 \mathrm{~nm}\) long. How many silicon atoms does this correspond to?
Short Answer
Expert verified
There are approximately 310 silicon atoms in the channel length of a Pentium 4 processor chip, given a channel length of 65 nm and a silicon atom diameter of 2.1 Å.
Step by step solution
01
Convert channel length to angstroms
Since the channel length is given in nanometers (nm) and the diameter of silicon atoms is given in angstroms (Å), we need to convert the channel length to angstroms. We know that 1 nm is equal to 10 Å, so we can convert 65 nm to angstroms using this conversion factor:
65 nm × (10 Å / 1 nm) = 650 Å
02
Look up the diameter of a silicon atom
We can look up the diameter of a silicon atom from a reliable source, such as a chemistry textbook or a scientific database. The diameter of a silicon atom is approximately 2.1 Å.
03
Calculate the number of silicon atoms in the channel length
Now that we have the channel length in angstroms (650 Å) and the diameter of a silicon atom (2.1 Å), we can calculate the number of silicon atoms that can fit in the channel length by dividing the length by the diameter of a single silicon atom:
Number of silicon atoms = (Channel length) / (Diameter of a silicon atom)
Number of silicon atoms = (650 Å) / (2.1 Å/atom)
04
Solve for the number of silicon atoms
Dividing 650 Å by 2.1 Å/atom, we get:
Number of silicon atoms ≈ 309.52
05
Round the number of silicon atoms to the nearest whole number
Since it's not possible to have a fraction of an atom, we'll round the number of silicon atoms to the nearest whole number:
Number of silicon atoms ≈ 310
Therefore, there are approximately 310 silicon atoms in the channel length of a Pentium 4 processor chip.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
angstroms to nanometers conversion
Understanding the conversion between angstroms and nanometers is vital in scientific calculations, particularly when dealing with atomic scales and semiconductor technology. An angstrom, denoted by the symbol Å, is a metric unit of length equal to one ten-billionth of a meter (\(10^{-10}\) meters) or 0.1 nanometers. Conversely, a nanometer (nm) is one billionth of a meter (\(10^{-9}\) meters).
This conversion is crucial when comparing measurements given in different units, such as the diameter of silicon atoms in angstroms.
- This means that 1 nanometer is equivalent to 10 angstroms.
- To convert a measurement from nanometers to angstroms, simply multiply the value in nanometers by 10.
This conversion is crucial when comparing measurements given in different units, such as the diameter of silicon atoms in angstroms.
channel length calculation
The channel length in a processor is a critical measurement as it determines the space within which electronic signals operate. It is typically expressed in nanometers in modern processors.
For a Pentium 4 processor with a 65 nm channel length:
- The process of calculating how many atoms fit into this channel length involves determining the physical space an atom occupies.
- Once the channel length is converted into the same unit as the atomic diameter (angstroms, in this case), it becomes easier to compute.
For a Pentium 4 processor with a 65 nm channel length:
- Convert the length to angstroms: 65 nm × 10 Å/nm = 650 Å.
- Given the silicon atom diameter of 2.1 Å, divide the channel length (650 Å) by the diameter (2.1 Å).
Pentium 4 processor
The Pentium 4 processor, first introduced by Intel in 2000, is known for a variety of technological advancements, including increased computing power and improved energy efficiency.
The smaller the channel length, the more compact the processor can be, leading to faster processing speeds due to the shorter distance for electrical signals.
This feature makes the Pentium 4 a fascinating subject for studying the impacts of reducing atomic and molecular scales on technological advancement.
- Notably, it demonstrates progress with the reduced scale of its microarchitecture, allowing more transistors to fit on a single chip.
- This advancement helps increase the processor's speed and efficiency.
The smaller the channel length, the more compact the processor can be, leading to faster processing speeds due to the shorter distance for electrical signals.
This feature makes the Pentium 4 a fascinating subject for studying the impacts of reducing atomic and molecular scales on technological advancement.
atomic dimensions
Atomic dimensions refer to the size or diameter of atoms, which is typically measured in angstroms. Understanding these dimensions is essential for technology fields that work at a microscopic or nanoscopic level.
It plays a crucial role in fields like semiconductor physics where atomic arrangements affect material properties and technological functionalities.
In essence, awareness of atomic dimensions is integral to the design and function of cutting-edge technology.
- An atom's diameter can vary depending on the element; for instance, silicon has a diameter of approximately 2.1 Å.
- These dimensions are pivotal when considering how many atoms fit into a specific space, such as the channel length in processors.
It plays a crucial role in fields like semiconductor physics where atomic arrangements affect material properties and technological functionalities.
In essence, awareness of atomic dimensions is integral to the design and function of cutting-edge technology.