An astrophysical source simultaneously emits X-ray radiation of wavelength λX=4.0×10−11 m\lambda_{\text{X}} = 4.0 \times 10^{-11} \text{ m}λX=4.0×10−11 m and infrared radiation of wavelength λIR=1.2×10−6 m\lambda_{\text{IR}} = 1.2 \times 10^{-6} \text{ m}λIR=1.2×10−6 m. Both waves travel through the vacuum of interstellar space.
Which of the following correctly identifies the ratio of their speeds, vXvIR\displaystyle \frac{v_{\text{X}}}{v_{\text{IR}}}vIRvX, and the ratio of their photon energies, EXEIR\displaystyle \frac{E_{\text{X}}}{E_{\text{IR}}}EIREX?
vXvIR=1\frac{v_{\text{X}}}{v_{\text{IR}}} = 1vIRvX=1, and EXEIR=3.3×10−5\frac{E_{\text{X}}}{E_{\text{IR}}} = 3.3 \times 10^{-5}EIREX=3.3×10−5
vXvIR=1\frac{v_{\text{X}}}{v_{\text{IR}}} = 1vIRvX=1, and EXEIR=3.0×104\frac{E_{\text{X}}}{E_{\text{IR}}} = 3.0 \times 10^4EIREX=3.0×104
vXvIR=3.0×104\frac{v_{\text{X}}}{v_{\text{IR}}} = 3.0 \times 10^4vIRvX=3.0×104, and EXEIR=1\frac{E_{\text{X}}}{E_{\text{IR}}} = 1EIREX=1
vXvIR=3.0×104\frac{v_{\text{X}}}{v_{\text{IR}}} = 3.0 \times 10^4vIRvX=3.0×104, and EXEIR=3.3×10−5\frac{E_{\text{X}}}{E_{\text{IR}}} = 3.3 \times 10^{-5}EIREX=3.3×10−5