Question

question 17 of 18
vitamin d is produced in the skin when 7 - dehydrocholesterol reacts with uvb rays (ultraviolet b) having wavelengths between 270 nm and 300 nm. what is the energy range ( e_{min } leq e leq e_{max } ) of the uvb photons?
( e_{min }=quad j quad e_{max }=quad j )

Explanation:

Step1: Recall the formula for photon energy

The energy of a photon is given by \(E = \frac{hc}{\lambda}\), where \(h = 6.626\times10^{-34}\space J\cdot s\) (Planck's constant) and \(c = 3\times 10^{8}\space m/s\) (speed of light).

Step2: Calculate \(E_{min}\)

For \(E_{min}\), we use the longest wavelength \(\lambda_{max}=300\space nm = 300\times10^{-9}\space m\)

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Step3: Calculate \(E_{max}\)

For \(E_{max}\), we use the shortest wavelength \(\lambda_{min} = 270\space nm=270\times 10^{-9}\space m\)

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Answer:

\(E_{min}=6.626\times 10^{-19}\space J\)
\(E_{max}\approx7.36\times 10^{-19}\space J\)