A star emits light with wavelength 120 nm. An observer on earth measures the wavelength of the light received from the star to be 600 nm. Calculate the speed with which the star is moving.

To calculate the speed with which the star is moving, we can make use of the Doppler effect. The Doppler effect describes the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave. In this case, the observer on Earth measures a longer wavelength of 600 nm, compared to the actual wavelength emitted by the star, which is 120 nm.

The Doppler effect equation for wavelength can be written as:

Δλ/λ = v/c

Where:
Δλ is the change in wavelength
λ is the original wavelength
v is the velocity of the source or observer
c is the speed of light in a vacuum

Since the observer on Earth measures a longer wavelength, we can determine the change in wavelength (Δλ) by subtracting the original wavelength (λ) from the measured wavelength:

Δλ = λ_observed - λ_emitted

In this case, Δλ = 600 nm - 120 nm = 480 nm.

Now, substituting the values into the Doppler effect equation:

Δλ/λ = v/c

480 nm / 120 nm = v / c

4 = v / c

To solve for v (the velocity of the star), we can rearrange the equation:

v = 4 * c

Plugging in the value for the speed of light in a vacuum, which is approximately 3 × 10^8 meters per second:

v = 4 * (3 × 10^8 m/s)
v = 1.2 × 10^9 m/s

Therefore, the speed with which the star is moving is approximately 1.2 × 10^9 meters per second.