Respuesta :
Answer:
(a). The velocity of star is [tex]8.1\times10^{6}\ m/s[/tex] and the direction of star toward the earth.
(b). The shift is 0.0168 nm.
Explanation:
Given that,
Wavelength of spectral line = 663 nm
Wavelength of spectral line in lab = 645 nm
(a). We need to calculate the velocity
Using doppler's effect
[tex]\Delta \lambda=\dfrac{v}{c}\lambda[/tex]
Where, [tex]\Delta\lambda[/tex]= change in wavelength
v = velocity
c = speed of light
Put the value into the formula
[tex]663-645=\dfrac{v}{3\times10^{8}}\times663[/tex]
[tex]v=\dfrac{3\times10^{8}(663-645)}{663}[/tex]
[tex]v=8144796.38\ m/s[/tex]
[tex]v=8.1\times10^{6}\ m/s[/tex]
The direction of star toward the earth.
(b). Speed = 7800 m/s
We need to calculate the shift
Using formula of shift
[tex]\Delta \lambda=\lambda(\sqrt{\dfrac{1+\dfrac{v}{c}}{1-\dfrac{v}{c}}}-1)[/tex]
Put the value into the formula
[tex]\Delta \lambda=645\times(\sqrt{\dfrac{1+\dfrac{7800}{3\times10^{8}}}{1-\dfrac{7800}{3\times10^{8}}}}-1)[/tex]
[tex]\Delta\lambda=0.0168\ nm[/tex]
This shift is small compare to the the movement of Earth around the sun.
Hence, (a). The velocity of star is [tex]8.1\times10^{6}\ m/s[/tex] and the direction of star toward the earth.
(b). The shift is 0.0168 nm.
