{"knowledge_schema": {"broad_category": "Astronomy \u2192 Cosmology \u2192 Redshift and Spectroscopy", "refinement": "This problem involves understanding the redshift phenomenon, particularly how it affects the observation of specific spectral lines due to the expansion of the universe.", "specific_scope": "The focus is on the 21 cm line of neutral hydrogen, originally at 1420 MHz, and determining the minimum redshift at which this line can still be observed with radio telescopes.", "goal": "Calculate the minimum redshift value that allows the 21 cm line to be detected, considering the effects of redshift on the frequency of the emitted radiation."}, "summary": "This problem pertains to the field of astronomy and cosmology, specifically the concept of redshift and its impact on the observation of spectral lines. The task is to determine the minimum redshift at which the 21 cm line of neutral hydrogen, originally at 1420 MHz, can be observed with radio telescopes. The answer indicates that at a redshift of z = 0.1, the frequency of the line shifts to a detectable range, allowing for observation. Understanding redshift is crucial for interpreting how light from distant objects is affected by the expansion of the universe."}