Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to equal the energy of a gamma-ray photon with energy $4.1 \times 10 ^ { - 13 } \mathrm {~J} ?$ A)1.0 × 10⁶ B)1.4 × 10⁸ C)6.2 × 10⁹ D)3.9 × 10³

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Quizplus · Accepted Answer

The energy of a photon is given by E = hf, where h is Planck's constant and f is the frequency of the photon. The frequency of a photon is given by c/λ, where c is the speed of light and λ is the wavelength of the photon. So, the energy of a photon is given by E = hc/λ.The energy of a gamma-ray photon with energy $4.1 \times 10 ^ { - 13 } \mathrm {~J} $ is:$$E = 4.1 \times 10 ^ { - 13 } \mathrm {~J}$$The wavelength of a visible-light photon with a wavelength of 500 nm is:$$\lambda = 500 \mathrm {~nm} = 500 \times 10 ^ { - 9 } \mathrm {~m}$$The energy of a visible-light photon with a wavelength of 500 nm is:$$E = hc/\lambda = (6.626 \times 10 ^ { - 34 } \mathrm {~J \cdot s})(3 \times 10 ^ { 8 } \mathrm {~m/s})/(500 \times 10 ^ { - 9 } \mathrm {~m}) = 3.98 \times 10 ^ { - 19 } \mathrm {~J}$$The number of visible-light photons with a wavelength of 500 nm that would be needed to equal the energy of a gamma-ray photon with energy $4.1 \times 10 ^ { - 13 } \mathrm {~J} $ is:$$N = E_\gamma/E_\mathrm{visible} = (4.1 \times 10 ^ { - 13 } \mathrm {~J})/(3.98 \times 10 ^ { - 19 } \mathrm {~J}) = 1.03 \times 10 ^ { 6 }$$So, the correct answer is A.

Gamma Rays Are Photons with Very High Energy 4.1×10−13 J?4.1 \times 10 ^ { - 13 } \mathrm {~J} ?4.1×10−13 J?

Gamma Rays Are Photons with Very High Energy $4.1 \times 10 ^ { - 13 } \mathrm {~J} ?$