The yellow line emitted by a helium discharge tube in the laboratory has a wavelength of 587 nm
The same yellow line in the helium spectrum of a star has a measured
wavelength of 590 nm.
Calculate the speed of the moving star.
Doppler effect
Frequency (observed) f=c/λ=3•10⁸/5.87•10⁻⁷=5.11•10¹⁴ Hz
Frequency (apparent) f´=c/λ´=3•10⁸/5.9•10⁻⁷=5.085•10¹⁴ Hz
f'=cf/(c+u)
u=c{(f/f´)-1} =1.53•10⁶ m/s
To calculate the speed of the moving star, we can use the Doppler effect equation. The Doppler effect describes the change in wavelength or frequency of a wave when the source or observer is in motion relative to the wave.
The equation for the Doppler effect is:
Δλ/λ = v/c
Where:
Δλ is the change in wavelength
λ is the original wavelength
v is the velocity of the source relative to the observer
c is the speed of light in a vacuum
In this case, the original wavelength (λ) of the yellow line emitted by a helium discharge tube is 587 nm, and the measured wavelength (Δλ) of the yellow line in the helium spectrum of the star is 590 nm.
Plugging in the values into the Doppler effect equation, we can solve for v (the velocity of the star):
(Δλ/λ) = v/c
(590 nm - 587 nm) / 587 nm = v / c
Now, we need to convert the wavelengths into meters so that they match the units of c (speed of light). 1 nm = 10^-9 m.
(3 x 10^-9 m) / (587 x 10^-9 m) = v / (3 x 10^8 m/s)
Simplifying the equation further:
0.0051 = v / (3 x 10^8 m/s)
To solve for v, we can rearrange the equation:
v = 0.0051 x 3 x 10^8 m/s
v = 1.53 x 10^6 m/s
Therefore, the speed of the moving star is approximately 1.53 x 10^6 m/s.