Answer:
The correct answer will be "2.97 × 10⁸ m/s".
Explanation:
The give values are:
Observed frequency, [tex]F=4.26\times 10^{10} \ Hz[/tex]
Original frequency, [tex]F_{0}=6.17\times 10^{14} \ Hz[/tex]
Let the velocity of Rigel be = V m/s
As we know,
⇒
[tex]F_{0}=F\sqrt{\frac{C+V}{C-V}}\\[/tex]
On putting the values, we get
⇒
[tex]\frac{6.17\times 10^{14} }{4.26\times 10^{10} } =\sqrt{\frac{C+V}{C-V} }[/tex]
⇒
[tex]\frac{C+V}{C-V}=(14483.56808)^2[/tex]
⇒
[tex]\frac{C+V}{C-V}=209773744.2[/tex]
⇒
[tex]C+V=209773744.2 \ C-209773744.2 \ V[/tex]
⇒
[tex]C-209773744.2 \ C=209773744.2 \ V-V[/tex]
⇒
[tex]V=\frac{209773743.2}{209773745.2} \ C[/tex]
⇒
[tex]V=0.99 \ C[/tex]
So that the Rigel's velocity will be "0.99 C".
Now,
⇒ [tex]V=0.99\times 3\times 10^8[/tex]
⇒ [tex]=2.97\times 10^8 \ m/s[/tex]
