Question

The diameter of a biscuit is approximately 51 millimeters (mm). An atom of bismuth (Bi) is approximately 320. picometers (pm) in diameter. Calculate the number of bismuth atoms needed to span the diameter of a biscuit in a line. Express your answer in scientific notation, showing the correct number of significant figures. (Enter your answer using one of the following formats: 1.2e-3 for 0.0012 and 1.20e+2 for 120.

Answer 1

To span the diameter of a biscuit with bismuth atoms, you divide the diameter of the biscuit in picometers by the diameter of a bismuth atom and then express it in scientific notation.

Step-by-step explanation:

To find out the number of bismuth atoms that can span the diameter of a biscuit, we need to convert the diameter of the biscuit from millimeters to picometers and then divide by the diameter of a bismuth atom.

First, convert the diameter of the biscuit to picometers:
51 mm = 51 × 10^3 × (10^3 pm/mm) = 51 × 10^6 pm.

Then, divide this by the diameter of a bismuth atom (320 pm):
Number of bismuth atoms = (51 × 10^6 pm) / (320 pm) = 1.59375 × 10^5.

Expressed in scientific notation with the correct number of significant figures we get 1.59 × 10^5 because the diameter of the biscuit was provided to three significant figures.

Answer 2

Bismuth atoms = 1,59375e+8

Step-by-step explanation:

Data: Biscuit diameter = 51 mm

Bismuth (Bi) atom diameter = 320 pm

We need to calculate the number of bismuth atoms needed to span the diameter of a biscuit in a line. First we need to choose a unit to work with. In this case i'm going to use picometers.

We transform the biscuit diameter to picometer by using a rule of three:

1 mm = 1e+9 pm ⇒ 51 mm = 5,1e+10 pm

`(1 mm)/(51 mm)=(1e+9 pm)/(x)`

x = 5,1e+10 pm

Remember that:

1 m = 1e+12 pm

1 cm = 1e+10 pm

1 mm = 1e+9 pm

Now we calculate how many Bismuth atoms we need to span the diameter of a biscuit in a line:

`Bismuth atoms = (5,1e+10 pm)/(320 pm)\\ Bismuth atoms = 1,59375e+8`