Question

Just after detonation, the fireball in a nuclear blast is approximately an ideal blackbody radiator with a surface temperature of about 0.84 × 10⁷ K. (a) Find the wavelength at which the thermal radiation is maximum and (b) identify the type of electromagnetic wave corresponding to that wavelength. This radiation is almost immediately absorbed by the surrounding air molecules, which produces another ideal blackbody radiator with a surface temperature of about 1.0 × 10⁵ K. (c) Find the wavelength at which the thermal radiation is maximum and (d) identify the type of electromagnetic wave corresponding to that wavelength.

Answer 1

Part A.

Using Wien's displacement law, the wavelength at which the thermal radiation is maximum is given by:

= 2.898*10^-3/T

Given that Blackbody radiator has a temperature of 0.84*10^7 K, So

= 2.898*10^-3/(0.84*10^7)

= 3.45*10^-10 m = wavelength

Part B.

So above wavelength lies in the X-ray region of electromagnetic spectrum.

Part C.

Using Wien's displacement law, the wavelength at which the thermal radiation is maximum is given by:

= 2.898*10^-3/T

Given that now new Blackbody radiator has a temperature of 1.0*10^5 K, So

= 2.898*10^-3/(1.0*10^5)

= 2.90*10^-8 m = wavelength

Part B.

So above wavelength lies in the Ultraviolet region of electromagnetic spectrum.

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