Here it is
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24 carat god is 100% Gold
22 carat is 22/24 x100% =91.67 %
In 0.450 gold ring
mass of gold is 91.67*0.450 /100
Now convert this mass to moles and then atoms.
= 0.4125  g . 1mole /197.0g . 6.022*10^23 atoms/1mole