Problem 52 - A Complete Resource Book in Chemistry for JEE Main

Question

Which is the correct order of micro, nano, femto and pico here? (a) micro \(<\) nano \(<\) pico \(<\) femto (b) pico \(<\) femto \(<\) nano \(<\) micro (c) femto \(<\) pico \(<\) nano \(<\) micro (d) femto \(<\) nano \(<\) micro \(<\) pico

Step-by-Step Solution

Answer

Option (c): Femto < Pico < Nano < Micro.

Step 1: Understand the Scientific Notation Prefixes

Before determining the order, we must understand what each prefix means in terms of scientific notation.- Micro (µ) means \( 10^{-6} \).- Nano (n) means \( 10^{-9} \).- Pico (p) means \( 10^{-12} \).- Femto (f) means \( 10^{-15} \).

Step 2: Arrange Prefixes by Power of Ten

Since we know what each prefix represents, we can arrange them in ascending order based on their power of ten.- The smallest value is Femto \( 10^{-15} \).- Then, we have Pico \( 10^{-12} \).- Next, there is Nano \( 10^{-9} \).- Finally, the largest value is Micro \( 10^{-6} \).

Step 3: Verify Matching with Given Options

Now, compare our sorted order, Femto \(<\) Pico \(<\) Nano \(<\) Micro, with each provided option.Option (c) suggests the order: Femto \(<\) Pico \(<\) Nano \(<\) Micro.This matches our calculated order.

Key Concepts

Understanding Micro

The prefix 'micro', denoted by the Greek letter µ, is a critical part of scientific measurement. In terms of scientific notation, micro refers to a factor of one millionth, or \( 10^{-6} \). This means that any unit of measure such as meters, grams, or liters, when prefixed by 'micro', is a million times smaller than the base unit.

This is particularly useful in fields like biology and electronics, where things are often too small to be easily measured in standard units. For example, a typical bacterium may be measured in micrometers (µm) because ordinary meters are far too large for such tiny organisms.

Understanding micro gives a strong foundation for grasping how scientific notation prefixes scale, making it easier to comprehend how much smaller the subsequent prefixes are.

Delving into Nano

The 'nano' prefix, symbolized by 'n', signifies a billionth, or \( 10^{-9} \), of any given base unit. Such precision is crucial when dealing with the extremely small dimensions in nanotechnology and molecular biology.

To put it in perspective, a human hair is approximately 80,000 to 100,000 nanometers wide. Nanometers (nm) allow scientists to measure and manipulate molecular and atomic scales effectively, revolutionizing fields like medicine and materials science.

Embracing the nano scale offers exciting new frontiers for research and technology, and it's fascinating just how much impact a billionth can have at such tiny scales.

Exploring Pico

'Pico' is a less commonly recognized prefix, represented by the letter 'p', indicating a trillionth, or \( 10^{-12} \). At this scale, measurement is incredibly precise and is used in contexts where extreme accuracy is crucial, such as photon physics and certain chemical reactions.

For instance, energy levels between atomic particles may be measured in picojoules. The picometer also finds its place in measuring atomic dimensions, providing insight into the very fabric of matter.

Pico provides a glimpse into the incredible power of scientific notation, enabling scientists to quantify and explore phenomena that are otherwise invisible to the naked eye.

Unveiling Femto

The prefix 'femto', denoted as 'f', translates to a quadrillionth, or \( 10^{-15} \). It’s the smallest of the four prefixes discussed here, used in very specialized scientific and engineering contexts.

One primary application of the femto scale is in particle physics. For example, the size of atomic nuclei is often measured in femtometers. Another example is the femtosecond, a unit of time crucial in studying chemical reactions at the molecular level, particularly those involving light (femtochemistry).

By understanding femto, we unlock the ability to observe and manipulate time and space at unimaginable scales, driving forward technological and scientific progress.