Question

If a spectral line from a distant star is measured to have a wavelength of 497.15 nm, but is normally at 497.22 nm how fast (speed, not velocity) with respect to the Earth is the star moving in m/s

Answer 1

Answer:

v = -4.22 x 10⁻⁴ m/s

Explanation:

given,

measured wavelength = 497.15 nm

Normally wavelength = 497.22 nm

Change in wavelength

Δ λ = 497.15 - 497.22

Δ λ = -0.07 nm

using Doppler's equation

$\dfrac{\Delta \lambda}{\lambda}=\dfrac{v}{c}$

v is the speed of the star

c is the speed of light

$\dfrac{-0.07\ nm}{497.22\ nm}=\dfrac{v}{3\times 10^8}$

      v = -4.22 x 10⁻⁴ m/s

Speed of the star moving is equal to v = -4.22 x 10⁻⁴ m/s

Answer 2

Answer:

The speed is 42210 m/s.

Explanation:

Given that,

Normally wavelength $\lambda= 497.22\ nm$

Observed spectral line $\Delta \lambda+\lambda= 497.15\ nm$

We need to calculate the change in wavelength

Using formula of wavelength

$\Delta \lambda+\lambda=497.15$

$\Delta\lambda+497.22=497.15$

$\Delta\lambda=497.15-497.22$

$\Delta\lambda=−0.07\ nm$

We need to calculate the value of z

Using formula for z

$z=\dfrac{\Delta\lambda}{\lambda}$

Put the value into the formula

$z=\dfrac{-0.07}{497.22}$

$z=−0.0001407$

We need to calculate the speed

Using formula of speed

$v=c\times z$

Put the value into the formula

$v=3\times10^{8}\times0.0001407$

$v=42210\ m/s$

Hence, The speed is 42210 m/s.