Question

Infrared telescope, which use special infrared dictators, are able to do peer farther into star-forming regions of the galaxy because infrared light is not scattered as strongly as is visible light by the tenuous clouds of hydrogen gas from which new stars are created. for what wavelength of light is the scattering only $1\%$that of light with visible wavelength of $500nm$?

Short answer

The wavelength of light is the scattering only $1\%$that of light with a visible wavelength of $500nm$is$1518nm$.

Step-by-step solution

Given information

We have given that:

$\lambda =500nm$.

We need to find the wavelength.

Simplification

As we know the intensity of scattered light depends inversely on the fourth power of the wavelength.

$I_{scattered}\alpha {\lambda }^{-4}$

From the Rayleigh scattering, we will get the wavelength of light is the scattering only $1\%$that of light with a visible wavelength of $500nm$

$0.01={\left(\frac{\lambda }{500}\right)}^4$

$\lambda =\frac{500}{\sqrt[4]{0.01}}$

$\lambda =1581nm.$

Hence the wavelength $1581nm$represents a short-range infrared region.