91影视

Let$f$represent the frequency detected by an observer moving with velocity$\stackrel{鈫�}{v}$relative to that rest frame. Then, when the direction of $\stackrel{鈫�}{v}$is directly away from the source.

Then the expression for the observed frequency is given by,

$f=f_0\sqrt{\frac{1鈭�尾}{1+尾}}$

The wavelength is inversely proportional to the frequency$(位鈭�f^{-1})$$(位鈭�f^{-1})$

. Thus,

$位={位}_0\sqrt{\frac{1+尾}{1鈭�尾}}$鈥︹�� (i)

The universe is expanding, with the distant galaxies moving away from us at a rate$v$ is given by Hubble鈥檚 law as,

$v=Hr$

Here$H$ is Hubble鈥檚 constant whose value is equal to,$0.0218\text{鈥尘/蝉}鈰�\text{鈥塴测}$,$r$is the distance to the galaxy and $v$is the recessional speed.

As, $v=尾c$

$鈬�尾=\frac{Hr}{c}$鈥︹�� (ii)

Substitute the values into the equation (ii)

$\begin{array}{c}尾=\frac{(0.0218)(2.40脳{10}^8)}{2.998脳{10}^8}\\ =0.017452\end{array}$

Substitute $656.3\text{鈥塶尘}$for ${位}_o$and$0.017452$for$尾$into the equation (i)

$\begin{array}{c}位=656.3\sqrt{\frac{1+0.017452}{1-0.017452}}\\ =668\text{鈥塶}m\end{array}$width="192">位=656.31+0.0174521-0.017452=668鈥塶m

Hence, the value of wavelength is 668 mm.