Question

what is the wavelength, in nm, of radiation which has an energy of 3.371 x 10^-19 joules per photon?

589.3 nm
655.9 nm
170.0 nm
745.1 nm
152.5 nm

Explanation:

Step1: Recall the energy - wavelength formula

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

Step2: Substitute the values

Substitute \(h = 6.626\times 10^{-34}\space J\cdot s\), \(c = 3\times 10^{8}\space m/s\), and \(E=3.371\times 10^{-19}\space J\) into the formula:

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Step3: Convert meters to nanometers

Since \(1\space m = 10^{9}\space nm\), then \(\lambda=(5.896\times 10^{-7}\space m)\times(10^{9}\space nm/m)=589.6\space nm\approx589.3\space nm\) (due to rounding differences in the constants used in different textbooks or calculators)

Answer:

A. \(589.3\space nm\)