Final answer:
To find the speed of the hydrogen gas moving away from us, we use the Doppler effect with the observed and emitted wavelengths. Following the Doppler shift formula and applying the given values suggest a speed significantly different from the provided options, possible due to an error in the provided data or options.
Step-by-step explanation:
To determine the speed of the hydrogen gas near the center of our galaxy, we use the Doppler effect. The observed wavelength (λobserved) is 1900 nm, and the emitted wavelength (λemitted) is 1875 nm. Using the formula for the Doppler shift, Δλ/λ = v/c, where Δλ is the change in wavelength, v is the velocity of the gas, and c is the speed of light, we substitute the given values to find v:
Δλ = λobserved - λemitted = 1900 nm - 1875 nm = 25 nm
v = Δλ/λemitted × c
v = (25 nm / 1875 nm) × 3 × 108 m/s
v = 4000 km/s
This calculation gives a speed that is not listed among the options provided, suggesting a possible mistake in the calculation or the options given. However, the method described is correct for finding the speed of a gas using the Doppler effect with redshifted wavelengths.