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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency $$1.20 \times {10^{15}}{\rm{ }}Hz$$?

The smallest detail observable is $$250\;nm$$.

See the step by step solution

## Step 1: Definition of frequency

Frequency is the number of waves that pass through a specific spot in a specific length of time.

## Step 2: Given information and Formula to be used

The frequency of ultraviolet light is: $$f = 1.20 \times {10^{15}}\;Hz$$

The speed of light value is: $$c = 3 \times {10^8}\;m/s$$

For an electromagnetic wave, the relationship between propagation speed, wavelength, and frequency is given by,

$$c = f\lambda$$

## Step 3: Calculate the wavelength

Consider the given values and simplify,

We have

$$\begin{array}{c}c = f\lambda \\3 \times {10^8} = 1.20 \times {10^{15}} \times \lambda \\\lambda = 250\;nm\end{array}$$

Therefore, the wavelength is $$250\;nm$$.