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# scientific notation

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Photons of red light have a wavelength of approximately 7*10^(-7) meters. The energy of a photon is inversely proportional to its wavelength. A photon with 8000 times the energy as a photon of red light will have a wavelength that can be written as a*10^b meters, where 1 <= a < 10. (In other words, in scientific notation.) What is a + b written as a decimal?

Apr 4, 2021

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Let the original photon with red light be $RP$, and the new photon with 8000 times the energy be $NP$.

Since $NP$ has $8000$ times the energy as $RP$, it has $\frac{1}{8000}$ times the wavelength of $RP$, because it is inversely proportional. The wavelength will then be $\frac{7*10^{-7}}{8*10^{3}}$

$\frac{7*10^{-7}}{8*10^{3}}=\frac{7}{8}*\frac{10^{-7}}{10^{3}}=\frac{7}{8}*10^{-10}=\frac{70}{8}*10^{-11}$(to get it in the format you want. Now,you have $a=\frac{70}{8}$ and $b=-11$, so $a+b=\boxed{-2.25}$

Apr 4, 2021