The James Webb Space Telescope detects infrared radiation from a distant galaxy at a wavelength of 1500 nm. Using the formula z = (λ_observed - λ_emitted)/λ_emitted, and knowing the emitted line corresponds to hydrogen alpha (656.3 nm), calculate the redshift z.
["Title: James Webb Space Telescope Measures Cosmic Redshift at 1500 nm: Unlocking Secrets of a Distant Galaxy", "---", "Introduction\nThe James Webb Space Telescope (JWST) continues to revolutionize our understanding of the universe by capturing breathtaking infrared data from the farthest reaches of space. Recently, JWST detected infrared radiation from a distant galaxy at a wavelength of 1500 nm, originating from hydrogen alpha emission—an essential signature of star-forming regions. This achievement not only showcases Webb’s unparalleled sensitivity but also provides valuable cosmological insights through redshift analysis.", "In this article, we explore how scientists calculate the redshift using precise wavelength measurements, offering a window into the expansion of the universe.", "---", "Understanding Redshift with JWST’s Infrared Discovery", "When astronomers observe distant galaxies, the light emitted from these objects shifts toward longer wavelengths as the universe expands—an effect known as cosmological redshift. By comparing the observed wavelength to the emitted wavelength, scientists determine the redshift z using the simple formula:", "[\nz = \frac{\lambda_{\ ext{observed}} - \lambda_{\ ext{emitted}}}{\lambda_{\ ext{emitted}}}\n]", "This dimensionless quantity reveals how much the universe has stretched since the light was released, offering clues about galactic distance, age, and cosmic evolution.", "---", "Calculation: JWST Detects Line at 1500 nm Emitted at 656.3 nm", "For a galaxy whose hydrogen alpha emission line (a crucial marker from ionized hydrogen) is observed at 1500 nm—longer than the emitted 656.3 nm—we compute the redshift as follows:", "- Observed wavelength:\n (\lambda_{\ ext{observed}} = 1500\ \ ext{nm})\n- Emitted wavelength (hydrogen alpha):\n (\lambda_{\ ext{emitted}} = 656.3\ \ ext{nm})", "Substitute into the formula:\n[\nz = \frac{1500\ \ ext{nm} - 656.3\ \ ext{nm}}{656.3\ \ ext{nm}} = \frac{843.7}{656.3} \approx 1.285\n]", "Thus, the redshift (z \approx 1.285) — a telling sign that this galaxy lies billions of light-years away, whose light has traveled for over 11 billion years.", "---", "Why This Redshift Matters", "A redshift of (z \approx 1.285) places the galaxy well in the early universe, when galaxies were still forming stars at rapid rates. JWST’s infrared detection of this hydrogen line confirms the presence of young, hot stars feeding vigorous star formation, even in galaxies existing over 12 billion years ago. Such findings help refine models of galaxy evolution and the epoch of reionization.", "---", "Conclusion", "The James Webb Space Telescope’s discovery of 1500 nm infrared radiation from a distant galaxy—and its redshift calculation using Hubble’s law principles—exemplifies cutting-edge astrophysics. By measuring gravitational and cosmological redshift, JWST opens new frontiers in how we observe, analyze, and comprehend the birth and growth of the universe’s most ancient structures.", "Stay tuned as JWST continues to delve deeper—and farther—into cosmic history, one infrared signal at a time.", "---", "Keywords: James Webb Space Telescope, infrared radiation, hydrogen alpha line, redshift z, cosmological redshift formula, galaxy evolution, Hubble’s law, star formation, JWST discoveries, hydrogen line shift, astrophysics, early universe, 1500 nm wavelength, z ≈ 1.285", "---", "Note: Redshift values like z ≈ 1.285 indicate a significant cosmic distance, consistent with galaxies observed at redshifts between 1 and 2, corresponding to a time when the universe was roughly 4–6 billion years old."]
