Lightning produces a maximum air temperature on the order of 9.3 \times 10^{3} K, whereas a nuclear explosion produces a temperature on the order of 9.2 \times 10^{6} K. Use Wien's displacement law to calculate the wavelength of the thermally-produced photons radiated with greatest intensity by each of these sources. Select the part of the electromagnetic spectrum where you would expect each to radiate most strongly. (a) lightning \lambda_{max}\approx nm b) nuclear explosion \lambda_{max}\approx pm

Lightning produces a maximum air temperature on the order of 9.3 \times 10^{3} K, whereas a nuclear explosion produces a temperature on the order of 9.2 \times 10^{6} K. Use Wien's displacement law to calculate the wavelength of the thermally-produced photons radiated with greatest intensity by each of these sources. Select the part of the electromagnetic spectrum where you would expect each to radiate most strongly. (a) lightning \lambda_{max}\approx nm b) nuclear explosion \lambda_{max}\approx pm

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asked 2021-05-18
Lightning produces a maximum air temperature on the order of \(\displaystyle{9.3}\times{10}^{{{3}}}{K}\), whereas a nuclear explosion produces a temperature on the order of \(\displaystyle{9.2}\times{10}^{{{6}}}{K}\). Use Wien's displacement law to calculate the wavelength of the thermally-produced photons radiated with greatest intensity by each of these sources. Select the part of the electromagnetic spectrum where you would expect each to radiate most strongly.
(a) lightning
\(\displaystyle\lambda_{{\max}}\approx{n}{m}\)
b) nuclear explosion
\(\displaystyle\lambda_{{\max}}\approx\pm\)

Answers (1)

2021-05-20
Given maximum are temperature on the order of \(\displaystyle{9}\cdot{3}\times{10}^{{{3}}}{K}\)
Nuclear explosion produces on temperature order of \(\displaystyle{9}\cdot{2}\times{10}^{{{6}}}{K}\)
a)We know that
\(\displaystyle{X}_{{\max}}=\frac{{{0}\cdot{2898}\times{10}^{{-{2}}}{m}{K}}}{{T}}\)
\(\displaystyle=\frac{{{0}\cdot{2898}\times{10}^{{-{2}}}{m}\cdot{K}}}{{{9}\cdot{3}\times{10}^{{{3}}}}}\)
\(\displaystyle={3}\cdot{116}\times{10}^{{-{7}}}{m}\)
\(\displaystyle={311}\cdot{6}\times{10}^{{-{9}}}{m}={311}\cdot{6}{n}{m}\)
b) \(\displaystyle\lambda_{{\max}}=\frac{{{0}\cdot{2898}\times{10}^{{-{2}}}{m}\cdot{K}}}{{T}}\)
\(\displaystyle=\frac{{{0}\cdot{2898}\times{10}^{{-{2}}}}}{{{9.2}\times{10}^{{{6}}}}}\)
\(\displaystyle={3}\cdot{15}\times{10}^{{-{10}}}{m}\)
\(\displaystyle={315}\cdot{0}\times{10}^{{-{12}}}{m}={315}\cdot{0}\pm\)
0

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