Question

Some diamonds appear yellow because they contain nitrogen compounds that absorb purple light of frequency 7.23 x 10¹⁴ Hz. Calculate the wavelength (in nm and Å) of the absorbed light.

Answer 1

Answer: The wavelength of the absorbed light is 415 nm or $4150\AA$

Explanation:

To calculate the wavelength of light, we use the equation:

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

where,

$\lambda$ = wavelength of the light  

c = speed of light = $3\times 10^8m/s$

$\nu$ = frequency of light = $7.23\times 10^{14}Hz=7.23\times 10^{14}s^{-1}$

Putting the values in above equation, we get:

$\lambda=\frac{3\times 10^8m/s}{7.23\times 10^{14}s^{-1}}=4.15\times 10^{-7}m$

Converting this into nanometers, we use the conversion factor:

$1m=10^9nm$

So, $4.15\times 10^{-7}m\times (\frac{10^9nm}{1m})=415nm$

Converting this into angstroms, we use the conversion factor:

$1m=10^{10}\AA$

So, $4.15\times 10^{-7}m\times (\frac{10^{10}\AA}{1m})=4150\AA$

Hence, the wavelength of the absorbed light is 415 nm or $4150\AA$