A carbon atom's nucleus and its electrons become separated by 20nm . How much work does it take to separate them in J?I found the magnitude of the force the nucleus feels from the electrons,2.07*10^-11 N but the work?
Could ex[lain me please?
Maurice,
I am having trouble too.
Well, well, well, it seems we have a separation crisis between an atom's nucleus and its electrons! Let me put on my scientific clown wig and help you out.
To find the work done in separating the carbon atom's nucleus and its electrons, we need to use the formula for work:
Work = Force × Distance
Since you already found the force (2.07 × 10^-11 N) and the distance of separation (20 nm = 20 × 10^-9 m), we can plug those values into the equation:
Work = 2.07 × 10^-11 N × 20 × 10^-9 m
Now, let's do some calculations:
Work = 4.14 × 10^-20 N·m
But we need to express it in joules, right? Well, by using the definition that 1 joule (J) is equal to 1 N·m, we can say that:
Work = 4.14 × 10^-20 J
Voila! There you have it, my scientific friend. The work required to separate the carbon atom's nucleus and its electrons is approximately 4.14 × 10^-20 joules.
To calculate the work done to separate the nucleus and electrons, you need to know the distance of separation (20nm) and the force between them (2.07*10^-11 N).
The work is given by the formula:
Work = Force × Distance
Plugging in the values:
Work = (2.07*10^-11 N) × (20 × 10^-9 m)
Note that 20nm is converted to meters by multiplying by 10^-9.
Calculating:
Work = 4.14*10^-10 N·m
Since the unit of work is joules (J), we need to convert N·m to J:
Work = 4.14*10^-10 J
Therefore, the work required to separate the nucleus and electrons is approximately 4.14*10^-10 J.
To calculate the work required to separate the carbon atom's nucleus and electrons, we can use the formula:
Work = Force x Distance
You've already found the magnitude of the force acting on the nucleus, which is 2.07 x 10^-11 N. To calculate the work, we need to determine the distance over which this force is applied.
You mentioned that the nucleus and electrons become separated by 20 nm (nanometers). To convert this distance to meters, we divide it by 1,000,000,000 (since there are 1 billion nanometers in a meter).
20 nm = 20 x 10^-9 m
Now we have both the force and the distance in SI units (meters), we can substitute them into the Work formula:
Work = (2.07 x 10^-11 N) x (20 x 10^-9 m)
Simplifying this equation, we get:
Work = (2.07 x 20) x (10^-11 x 10^-9) J
First, multiply the numbers outside the parentheses:
Work = 41.4 x 10^-20 J
Then, multiply the numbers inside the parentheses:
Work = 41.4 x 10^-20 J
Finally, simplify the expression:
Work = 4.14 x 10^-19 J
Therefore, it takes approximately 4.14 x 10^-19 joules of work to separate a carbon atom's nucleus and its electrons.