Given: diameter of the atomic nucleus of a lead atom is 1.75 × 10-15 m. What is its nucleus volume?
Just using
V = (4/3)π r^3
= (4/3)π(1.75 x 10^-15)^3
= (4/3)π(5.359375)(10)^-45
= 22.449 x 10^-45
= 2.2449 x 10^-44 m^3
Well, prepare yourself for some small talk! The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Since we know the diameter, which is twice the radius, we can simply divide it by 2 to get the radius. So, the radius of the atomic nucleus of a lead atom is 1.75 × 10-15 m ÷ 2. Now, plug it into the formula and let's embark on this tiny adventure!
To find the volume of the atomic nucleus, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere.
First, let's find the radius of the nucleus. Since the diameter is given, we can divide it by 2 to get the radius:
radius = (1.75 × 10^(-15) m) / 2
radius = 8.75 × 10^(-16) m
Now we can substitute the radius into the volume formula:
V = (4/3) * π * (8.75 × 10^(-16) m)^3
Calculating this expression will give us the volume of the nucleus.
To find the volume of the atomic nucleus, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Where:
V is the volume of the sphere (nucleus)
π is a mathematical constant (approximately 3.14159)
r is the radius of the sphere (half of the diameter)
Given that the diameter of the atomic nucleus of a lead atom is 1.75 × 10^(-15) m, we can first calculate the radius by dividing the diameter by 2:
r = (1.75 × 10^(-15) m) / 2
Next, we substitute the radius into the volume formula:
V = (4/3) * π * (r^3)
Let's perform the calculations:
r = (1.75 × 10^(-15) m) / 2 = 8.75 × 10^(-16) m
V = (4/3) * 3.14159 * (8.75 × 10^(-16) m)^3
Now you can use a calculator to find the volume V.