Question

You know that certain blackbody emits maximum radiation at 500 nm. How will the wavelength change if you decrease the temperature of the blackbody by 1000K? Where will the wavelength and frequency be now?

Answer 1

According to the wein's displacement law , temperature and wavelength is related by

where b =  2.8977729×10⁻³ m⋅K

and T is absolute in kelvins .

so given here for blackbody = 500 nm

so if the is at 500 nm so where will be the temperature at that instant

we have to calculate the temperature at that instant by wein's displacement law

T = (2.8977729×10⁻³) / 500 x 10^-9 = 5795.5458 K

so the temperature for now at 500 nm is 5795.54 kelvins.

if temperature is decreased by 1000 K , the temperature would be 4795.54 K .

for this temperature we have the as by the weins displacement law

= (2.8977729×10⁻³) / 4795.54 = 604.26 nm

so the radiation of the blackbody increases according to the wein's displacement law.

now the wavelength becomes 604.26 nm.

for frequency we have wavelength and frequency relation as

where is frequency and c is speed of light .

so    = (2.998 x 10⁸ )/ 604.26 x 10^-9 = 4.96 x 10¹⁴ Hz

now the wavelength becomes 604.26 nm and frequency becomes 4.96 x 10¹⁴ Hz.