Question

Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 7.158 g, is pressed into a leaf of 2.810 μm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.600 μm, what is the length of the fiber?

Answer 1

To find the area of the gold leaf, divide the mass of the gold sample by the product of its density and thickness. To find the length of the gold fiber, divide the mass of the gold sample by the product of its density, pi, and the square of its radius.

Step-by-step explanation:

To find the area of the gold leaf, we'll use the formula:

Area = Mass / (Density * Thickness)

Plugging in the values, we have:

Area = 7.158 g / (19.32 g/cm³ * 2.810 μm)

Converting the thickness to cm and solving the equation, we find that the area of the leaf is approximately 9.404 x 10^-4 cm².

To find the length of the gold fiber, we'll use the formula:

Length = Mass / (Density * π * Radius²)

Plugging in the values and converting the radius to cm, we have:

Length = 7.158 g / (19.32 g/cm³ * 3.1416 * (2.600 μm / 10⁴ cm/μm)²)

Solving the equation, we find that the length of the fiber is approximately 1.272 cm.

Answer 2

area of the leaf is 0.13167 m²

length of the fiber is 17431.1235 m

Step-by-step explanation:

Given data

gold density = 19.33 g/cm3

gold mass = 7.158 g

thickness = 2.810 μm = 2.810 ×
`10^(-6)` m

radius = 2.600 μm

to find out

area of the leaf and length of the fiber

solution

first we calculate volume from density

we know density formula that is mass / volume

so volume = mass / density

put these value

volume = 7.158 / 19.33

volume = 0.370 cm³ = 0.370 ×
`10^(-6)` m³

so area = volume / thickness

area = 0.370 ×
`10^(-6)` / 2.810 ×
`10^(-6)`

area = 0.13167 m²

and

area of fiber is = πr²

so area = π(2.600×
`10^(-6)` )²

area = 2.12264 ×
`10^(-11)`

so length = volume / area

put value

length = 0.370 ×
`10^(-6)` / 2.12264 ×
`10^(-11)`

length is 17431.1235 m