A distance galaxy is moving away from us at a speed of 47380367 m/s. For hydrogen gas in this galaxy, calculate the wavelength (in nm) to one decimal place of the hydrogen alpha line as observed here on earth. Note: This wavelength emitted by hydrogen is measured in the first year physics lab to be 656.2 nm.
Question
A distance galaxy is moving away from us at a speed of 47380367 m/s. For hydrogen gas in this galaxy, calculate the wavelength (in nm) to one decimal place of the hydrogen alpha line as observed here on earth. Note: This wavelength emitted by hydrogen is measured in the first year physics lab to be 656.2 nm.
Solution 1
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Solution 2
To solve this problem, we need to use the Doppler effect formula for light:
λ_observed = λ_emitted * (1 + v/c)
where: λ_observed is the observed wavelength, λ_emitted is the emitted wavelength, v is the velocity of the source relative to the observer, c is the speed of light in a vacuum.
Given: λ_emitted = 656.2 nm, v = 47380367 m/s, c = 299792458 m/s (speed of light).
Substituting these values into the formula, we get:
λ_observed = 656.2 nm * (1 + 47380367 m/s / 299792458 m/s)
Calculating the value inside the brackets first:
1 + 47380367 m/s / 299792458 m/s = 1.158
Then multiply this by the emitted wavelength:
λ_observed = 656.2 nm * 1.158 = 759.7 nm
So, the observed wavelength of the hydrogen alpha line from this distant galaxy here on Earth is 759.7 nm to one decimal place.
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