Question

A starlike object moves at the tremendous speed of 75000km/s! An analysis of the spectrum from the object indicates a strong red shift. What is the measured wavelength of the Lβ line for hydrogen?

Answer in nm

Answer 1

To calculate the measured wavelength of the Lβ line for hydrogen considering the redshift, we can use the relativistic Doppler effect formula:

λ_observed = λ_rest * sqrt((1 + v/c) / (1 - v/c))

Where:

λ_observed is the observed wavelength

λ_rest is the rest wavelength

v is the velocity of the starlike object

c is the speed of light in vacuum

The rest wavelength of the Lβ line for hydrogen is approximately 102.57 nm.

Now let's calculate the observed wavelength:

v = 75000 km/s = 75000 * 1000 m/s = 7.5 * 10^7 m/s

c = 3 * 10^8 m/s

λ_observed = 102.57 nm * sqrt((1 + 7.5 * 10^7 / (3 * 10^8)) / (1 - 7.5 * 10^7 / (3 * 10^8)))

Calculating the above expression, we find:

λ_observed ≈ 102.57 nm * sqrt(1.4083333)

λ_observed ≈ 102.57 nm * 1.1865502

λ_observed ≈ 121.77 nm

Therefore, the measured wavelength of the Lβ line for hydrogen, considering the redshift, is approximately 121.77 nm.