Question

Speed of light in vacuum is $3\times {10}^8\text{m/s}$. The range of wavelength of ultraviolet light is $50{\text{A}}^{\circ }-4000{\text{A}}^{\circ }$. What will be the range of frequency of ultraviolet light?

• A. $[4.28\times {10}^{14}\text{Hz}-9.8\times {10}^{16}\text{Hz}]$
  
• B. $[5\times {10}^{14}\text{Hz}-6\times {10}^{15}\text{Hz}]$
  
• C. $[7.5\times {10}^{14}\text{Hz}-6\times {10}^{16}\text{Hz}]$
  
• D. $[7\times {10}^{15}\text{Hz}-6\times {10}^{16}\text{Hz}]$
  

Answer 1

The correct option is C $[7.5\times {10}^{14}\text{Hz}-6\times {10}^{16}\text{Hz}]$


We know, if $f$ = frequency, $\lambda$ = wave length and $v$ = speed of light in vacuum.
then, $v=f\lambda$ or $f=\frac{v}{\lambda }$

So, for maximum frequency, $f_{max}=\frac{v}{{\lambda }_{min}}$

Substituting the given data,

$f_{max}=\frac{3\times {10}^8}{50\times {10}^{-10}}=6\times {10}^{16}\text{Hz}$

and minimum frequency, $f_{min}=\frac{v}{{\lambda }_{max}}$

Substituting the given data,

$f_{min}=\frac{3\times {10}^8}{4000\times {10}^{-10}}=7.5\times {10}^{14}\text{Hz}$

So, Range of frequencies of ultraviolet light will be $[7.5\times {10}^{14}\text{Hz}-6\times {10}^{16}\text{Hz}]$

$\begin{array}{c}\text{Why this Question}?\\ \text{This question teaches the student how to use the relation between frequency and wavelength.}\\ \text{It also introduces the concept of ultraviolet light as a subset of the electromagnetic spectrum}\end{array}$