The molar extinction coefficient is 15,200
.
The formula to be used to calculate molar extinction coefficient is -
A = ξcl, where A represents absorption, ξ refers molar extinction coefficient, c refers to concentration and l represents length.
The given values are in required units, hence, there is no need to convert them. Directly keeping the values in formula to find the value of molar extinction coefficient.
Rewriting the formula as per molar extinction coefficient -
ξ = 
ξ = 
Performing multiplication in denominator to find the value of molar extinction coefficient
ξ =
Performing division to find the value of molar extinction coefficient
ξ = 15,200 
Hence, the molar extinction coefficient is 15,200
.
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Number of Atoms in Gold for given mass can be calculated using following formula,
# of Moles = Number of Atoms / 6.022 × 10²³
Or,
Number of Atoms = Moles × 6.022 × 10²³ ------- (1)
Calculating Moles,
As,
Moles = Mass / M.mass
So,
Moles = 4.25 g / 196.96 g/mol
Moles = 0.0215
Putting value of mole in eq.1,
Number of Atoms = 0.0215 × 6.022 × 10²³
Number of Atoms = 1.299 × 10²²
Result:
4.25 g of Gold Nugget contains 1.299 × 10²² Atoms.
Use M x V = M' x V'
0.300 x V = 0.100 x 250
V = .......... ml