Given low-spin complexes:

$${K_3}\left[ {Co{{(N{O_2})}_6}} \right] - $$ Yellow colour

$${K_4}\left[ {Fe{{(CN)}_6}} \right] - $$ light yellow colour

$${K_3}\left[ {Fe{{(CN)}_6}} \right] - $$ bright red colour not yellow.

$$C{u_2}\left[ {Fe{{(CN)}_6}} \right] - $$ reddish brown color not yellow

$$Z{n_2}\left[ {Fe{{(N{O_2})}_6}} \right] - $$ bluish-white colour not yellow

$${K_3}\left[ {Co{{(N{O_2})}_6}} \right]$$

Oxidation state of $$Co: + 3$$

Configuration:

$$Co\,{d^7}\,{s^2}$$

$$C{o^{3 + }}\,{d^6}$$

$$3( + 1) + x + 6( - 1) = 0$$

$$3 + x - 6 = 0$$

$$x = 6 - 3 = + 3$$

For low-spin d$^6$ configuration, no unpaired electrons are present :

spin-only magnetic moment, $$\mu = \sqrt {n(n + 2)} $$

$$n = 0$$, $$\mu = 0$$

This complex shows yellow colour (bright yellow)

$${K_4}\left[ {Fe{{(CN)}_6}} \right]$$

Oxidation state of $$Fe: + 2$$

$$4( + 1) + x + 6( - 1) = 0$$

$$4 + x - 6 = 0$$

$$x = 6 - 4 = + 2$$

Configuration:

$$Fe\,{d^6}\,{s^2}$$

$$F{e^{ + 2}}\,{d^6}$$

$$\mu = 0$$

For low-spin d$^6$ configuration, no unpaired electrons are present :

This complex shows yellow colour (light yellow)

$${K_3}\left[ {Fe{{(CN)}_6}} \right]$$

Oxidation state of $$Fe: + 3$$

$$3( + 1) + x + 6( - 1) = 0$$

$$3 + x - 6 = 0$$

$$x = 6 - 3 = + 3$$

Configuration:

$$Fe\,{d^6}\,{s^2}$$

$$F{e^{ + 2}}\,{d^5}$$

low spin d$^5$

One unpaired electron is present.

Spin-only magnetic moment, $$\mu = \sqrt {n(n + 2)} $$

n (number of unpaired electrons) = 1

So, $$\mu = \sqrt {n(n + 2)} $$

$$ = \sqrt {1 \times 3} $$

$$ = \sqrt 3 $$

= 1.732 BM

Colour of the complex is not yellow.

$$C{u_2}\left[ {Fe{{(CN)}_6}} \right],\,C{u^{2 + }}$$ and $${\left[ {Fe{{(CN)}_6}} \right]^{4 - }}$$

$$x + 6( - 1) = - 4$$

$$x = - 4 + 6$$

$$ = + 2$$

Oxidation state of $$Fe: + 2$$

Configuration:

$$Fe\,{d^6}\,{s^2}$$

$$F{e^{2 + }}\,{d^6}$$

For low-spin d$^6$ configuration, no unpaired electrons are present

$$n = 0,\mu = \sqrt {n(n + 2)} = 0$$

Colour of the complex is not yellow.

$$Z{n_2}\left[ {Fe{{(CN)}_6}} \right]$$

$${\left[ {Fe{{(CN)}_6}} \right]^{4 - }}$$ and $$Z{n^{2 + }}$$

$$x + 6( - 1) = - 4$$

$$x = - 4 + 6 = + 2$$

Oxidation state of $$Fe: + 2$$

Configuration:

$$Fe\,{d^6}\,{s^2}$$

$$F{e^{2 + }}\,{d^6}$$

For low-spin d$^6$ configuration, no unpaired electrons are present.

$$n = 0,\,\mu = \sqrt {n(n + 2)} = 0$$

Colour of the complex is not yellow

The complexes having yellow colour are $${K_3}\left[ {Co{{(N{O_2})}_6}} \right]$$ and $${K_4}\left[ {Fe{{(CN)}_6}} \right]$$

The sum of the spin-only magnetic moment values of complexes having yellow colour is 0 (zero).