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Expert-verifiedApproximately 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 \(250\;nm\).
Frequency is the number of waves that pass through a specific spot in a specific length of time.
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,
\(c = f\lambda \)
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 \(250\;nm\).
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