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Just after detonation, the fireball in a nuclear blast is approximately an ideal blackbody radiator with a surface temperature of about 1.0107K.

(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 1.0105K.

(c) Find the wavelength at which the thermal radiation is maximum and (d) identify the type of electromagnetic wave corresponding to that wavelength.

Short Answer

Expert verified

Thus, (a) the wavelength of thermal radiation is maximum at7.75鈥夆赌媝尘 .

(b) the wavelength is 1.24鈥夆赌媙尘.

(c) the wavelength of thermal radiation is 7.75鈥夆赌媝尘.

(d) the wavelength is 1.24鈥夆赌媙尘.

Step by step solution

01

(a) The wavelength of thermal radiation is maximum.

Use the value formula then it gives by the de Broglie wavelength of the electron is:

=hp=h2meK=hc2meeV=6.6261034Js2(9.1091031kg)(1.6021019C)(25.0103V)=7.751012m=7.75鈥夆赌媝尘

Hence, the wavelength of thermal radiation is maximum at 7.75鈥夆赌媝尘.

02

(b) The type of magnetic wave corresponding to the wavelength.

A photon鈥檚 de Broglie wavelength is equal to its familiar wave relationship value. Use the valuehc=1240鈥媏痴nm gives:

=hcE=1240eVnm1.00keV=1.24鈥夆赌媙尘

Hence, the wavelength is 1.24鈥夆赌媙尘.

03

(c) The wavelength of thermal radiation is maximum at temperature 1.0×105K. 

The neutron mass equals to 1.6751027kg. Using the conversion from electronvolts to Joules gives;

=hp=h2meK=hc2meeV=6.6261034Js2(9.1091031kg)(1.6021019C)(25.0103V)=7.751012m=7.75鈥夆赌媝尘

Hence, the wavelength of thermal radiation is7.75鈥夆赌媝尘 .

04

(d) The type of magnetic wave corresponding to the wavelength at temperature 1.0×105K

A photon鈥檚 de Broglie wavelength is equal to its familiar wave relationship value. Use the valuehc=1240鈥媏痴nm gives:

=hcE=1240eVnm1.00keV=1.24鈥夆赌媙尘

Hence, the wavelength is 1.24鈥夆赌媙尘.

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