Question

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

Short answer

The smallest detail observable is \(250\;nm\).

Step-by-step solution

Definition of frequency

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

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,

\(c = f\lambda \)

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 \(250\;nm\).