ne kilogram of ice of density 1000 kg m–3 is frozen in the shape of a cube. The diameter of a water molecule is 10–10 m. What is the difference in the orders of magnitude of the length of one side of the ice cube and the diameter of a water molecule?
please and thank u
The volume of 1kg ice is:
V = mass/density = 1/1000 = 10⁻³ m³
A cube with sides of length L has a volume = L³
So for the ice cube:
L³ = 10⁻³
L = ∛(10⁻³) = 10⁻¹m
The ratio (length of ice cube)/(diameter of molecule)
= (10⁻¹)/(10⁻¹⁰)
= 10⁹
We say the length of a side of the ice cube is
*** 9 orders of magnitude ***
bigger than the diameter of the water molecule.
Or we can say there are 9 orders of magnitude difference between the length of one side of the ice cube and the diameter of a water molecule.
flirty me/ supercute -- please keep the same name for your posts.
use the second phrase.
Well, to find the difference in orders of magnitude, we need to compare the two values.
Let's start with the length of one side of the ice cube. We know that the density of ice is 1000 kg/m³ and the mass is 1 kilogram. Since density is mass divided by volume, we can calculate the volume of the ice cube using the formula V = m / ρ, where V is volume, m is mass, and ρ is density.
Given that the density is 1000 kg/m³ and the mass is 1 kilogram, we have V = 1 kg / 1000 kg/m³ = 0.001 m³.
Now, since the ice cube is a cube shape, all sides have the same length. Let's call the length "L."
So, V = L³, where V is the volume and L is the length of one side of the ice cube.
Substituting the value of V we calculated earlier, we get 0.001 m³ = L³. Solving for L, we find L ≈ 0.1 m.
Now, let's move on to the diameter of a water molecule, which is given as 10⁻¹⁰ m.
To find the difference in orders of magnitude, we compare the exponents. The exponent for 0.1 m is 0, and the exponent for 10⁻¹⁰ m is -10.
So, the difference in orders of magnitude is 10 - 0 = 10.
Therefore, the difference in the orders of magnitude of the length of one side of the ice cube and the diameter of a water molecule is 10.
Hope that didn't melt your brain!
To find the difference in the orders of magnitude between the length of one side of the ice cube and the diameter of a water molecule, we need to determine the magnitude of each value first.
1. Length of one side of the ice cube:
Given that the ice cube has a density of 1000 kg m^-3, we can calculate its volume using the mass of the ice cube, which is 1 kilogram.
Since density = mass/volume, we can rearrange the formula to solve for volume: volume = mass/density.
The volume of the ice cube is therefore 1 kg / 1000 kg m^-3 = 0.001 m^3.
Since the ice cube is in the shape of a cube, all sides have equal length. Thus, the length of one side of the ice cube is the cube root of the volume: (0.001 m^3)^(1/3) = 0.1 m.
2. Diameter of a water molecule:
The diameter of a water molecule is given as 10^-10 m.
Now, let's find the difference in the orders of magnitude:
To determine the order of magnitude, we need to count the number of zeros after the first non-zero digit in scientific notation.
For the length of one side of the ice cube, the order of magnitude is 0, since there are no zeros after the decimal point.
For the diameter of a water molecule, it is given as 10^-10 m. The order of magnitude is -10, as there are 10 zeros after the decimal point.
Finally, subtracting the orders of magnitude, we get:
0 - (-10) = 10.
Therefore, the difference in the orders of magnitude of the length of one side of the ice cube and the diameter of a water molecule is 10.