Gamma rays are photons with very high energy. What is the wavelength of a gamma-ray photon with energy $7.7 \times 10 ^ { - 13 } \mathrm {~J}$ ? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$
A) $2.6 \times 10 ^ { - 13 } \mathrm {~m}$
B) $3.5 \times 10 ^ { - 13 } \mathrm {~m}$
C) $3.9 \times 10 ^ { - 13 } \mathrm {~m}$
D) $3.1 \times 10 ^ { - 13 } \mathrm {~m}$

Question

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 wavelength of a photon is given by $\lambda = c/f$, where $c$ is the speed of light. Substituting the given values into these equations, we get:$$E = hf = \frac{hc}{\lambda}$$$$\lambda = \frac{hc}{E} = \frac{(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s})(3.0 \times 10^8 \mathrm{~m/s})}{7.7 \times 10^{-13} \mathrm{~J}} = 2.6 \times 10^{-13} \mathrm{~m}$$Therefore, the wavelength of the gamma-ray photon is $2.6 \times 10^{-13} \mathrm{~m}$.

Gamma Rays Are Photons with Very High Energy 7.7×10−13 J7.7 \times 10 ^ { - 13 } \mathrm {~J}7.7×10−13 J

Gamma Rays Are Photons with Very High Energy $7.7 \times 10 ^ { - 13 } \mathrm {~J}$