# The hydrogen Balmer line of quasar 3C273 is observed to have a wavelength of 563.9 nm. The laboratory hydrogen Balmer line is known to be 486.1 nm. What is the speed at which this quasar is moving away from us expressed in meters per second?

Jul 10, 2016

$v = 47521086.19625592$ m /sec. or $47521.08619625592$

#### Explanation:

To Obtain the receding speed of the quasar you first wil need to determine the red-shift of that quasar.

As,

The observed wavelength is 563.9 nm and the laboratory wavelength is found to be 486.1 nm you can determine the red-shift by the following expression.

Z = ($\lambda \left(o\right)$ - lambda(L))/ ($\lambda \left(L\right)$)

z = 563.9 - 486.1/ 486.1

The obtained red-shift is 0.1584036206541864
Now to obtain the speed you can use the following relationship:

Z = $\frac{v}{c}$

Where,

V is the recession velocity.

C is the speed of light

Z is the red-shift

$v = z \cdot c$

$v = 0.1584036206541864 \cdot 300 , 000 , 000$

$v = 47521086.19625592$ m /sec.