The relationship between wavelength, frequency and speed of an electromagnetic wave is given by
[tex]c= \lambda f[/tex]
where
c is the speed of light
[tex]\lambda[/tex] is the wavelength
f is the frequency
The infrared radiation of our problem has frequency [tex]f=9.76 \cdot 10^{13}Hz[/tex], therefore if we re-arrange the previous equation we can calculate its wavelength:
[tex]\lambda= \frac{c}{f}= \frac{3 \cdot 10^8 m/s}{9.76 \cdot 10^{13} Hz}=3.07 \cdot 10^{-6} m [/tex]
and converted into nanometers,
[tex]\lambda=3070 nm[/tex]
