Chapter 5, Problem 46A

Interpretation Introduction

Interpretation:

The wavelength and type of electromagnetic radiation with a frequency of $5.00\times {10}^{12}Hz$ needs to be determined.

Concept introduction:

The distance between two nearest crests or nearest troughs is called the wavelength. It is denoted by $\lambda$ (lambda) and is measured is terms of centimeter ( $cm$ ), Angstrom ( $\AA$ ), micron( $\mu$ ) or nanometre ( $nm$ ).

Answer to Problem 46A

Wavelength is $6\times {10}^4\text{ nm}$ and wave belongs to infrared region.

Explanation of Solution

Given information:

The given frequency $\left(\nu \right)=5.00\times {10}^{12}Hz$.

Calculation:

Frequency is related to wavelength as follows:

$\lambda =\frac{c}{\nu }$

Where,

$\lambda =$ wave length

$c=$ velocity of light

$\nu =$ frequency

Putting the values,

$\begin{array}{l}\lambda =\frac{3\times {10}^{8}m/s}{5\times {10}^{12}Hz}=0.6\times {10}^{-4}m=6.0\times {10}^{-5}m\left(\frac{{10}^9\text{ nm}}{1\text{ m}}\right)\\ =6\times {10}^4\text{ nm}\end{array}$

Wave with wave length $6\times {10}^4\text{ nm}$ belongs to infrared region.

Conclusion

Wavelength is $6\times {10}^4\text{ nm}$ and wave belongs to infrared region.