# 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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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
$$\displaystyle\lambda_{{\max}}\approx\pm$$

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) $$\displaystyle\lambda_{{\max}}=\frac{{{0}\cdot{2898}\times{10}^{{-{2}}}{m}\cdot{K}}}{{T}}$$
$$\displaystyle=\frac{{{0}\cdot{2898}\times{10}^{{-{2}}}}}{{{9.2}\times{10}^{{{6}}}}}$$
$$\displaystyle={3}\cdot{15}\times{10}^{{-{10}}}{m}$$
$$\displaystyle={315}\cdot{0}\times{10}^{{-{12}}}{m}={315}\cdot{0}\pm$$

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