A system of 1216 particles, each of which is either an electron or a proton, has a net charge of -5.920×10-17 C.
A)How many electrons are in this system (exactly)?
B)What is the mass of this system (to three significant digits)?
A) How many electrons are in this "electron party"? Well, we know that the total charge of the system is -5.920×10-17 C.
Since electrons have a charge of -1.602 x 10^(-19) C, we can calculate the number of electrons using the formula:
Number of electrons = Total charge / Charge per electron
Number of electrons = (-5.920×10^(-17) C) / (-1.602 x 10^(-19) C)
Now, let me grab my trusty calculator... *beep boop beep* Crunching the numbers... And voila!
The exact number of electrons in this system is approximately 369. The "electron club" just got a little more crowded!
B) Now let's move on to the mass of this system. We don't know the exact mass of each particle, but we do know the masses of electrons and protons. However, the difference is quite significant - an electron is about 1/1836 times the mass of a proton. So, we'll use the average mass.
The average mass of a particle in this system can be calculated using the formula:
Average Mass = (Total Mass of Electrons + Total Mass of Protons) / Total Number of Particles
Now, let's calculate it.
Assuming the mass of an electron is 9.10938356 x 10^(-31) kg and the mass of a proton is 1.67262192 x 10^(-27) kg, we can calculate the average mass:
Average Mass = (Number of Electrons * Mass of Electrons + Number of Protons * Mass of Protons) / Total Number of Particles
Again, let me see... *beep boop beep* Crunching the numbers...
The mass of this system, rounded to three significant digits, is approximately 1.407 x 10^(-28) kg. It may be light as a feather, but it still deserves a round of applause! *claps* Bravo!
A) To find the number of electrons in the system, we need to calculate the total charge due to the electrons, and then divide it by the charge of a single electron.
Each electron has a charge of -1.602 × 10^-19 C (the negative sign indicates the charge of an electron). Therefore, to find the number of electrons, we can divide the total charge by the charge of a single electron:
Number of electrons = Total charge / Charge of a single electron
Number of electrons = -5.920 × 10^-17 C / (-1.602 × 10^-19 C)
Number of electrons ≈ 36.8
So, there are approximately 36.8 electrons in this system.
B) To find the mass of the system, we need to consider the masses of the electrons and protons within it. The mass of an electron is approximately 9.109 × 10^-31 kg, and the mass of a proton is approximately 1.673 × 10^-27 kg.
To calculate the total mass, we need to multiply the number of electrons by the mass of an electron, and multiply the number of protons by the mass of a proton. Then, we can sum these two values:
Total mass = (Number of electrons × Mass of electron) + (Number of protons × Mass of proton)
Using the previously calculated number of electrons (approximately 36.8), we can substitute the values into the equation:
Total mass = (36.8 × 9.109 × 10^-31 kg) + (1216 - 36.8) × 1.673 × 10^-27 kg)
Total mass ≈ 3.352 × 10^-28 kg
Therefore, the mass of this system, to three significant digits, is approximately 3.35 × 10^-28 kg.
A) To find the number of electrons in the system, we need to know the charge of a single electron. The charge of an electron is -1.602 × 10^(-19) C. By dividing the total net charge of the system by the charge of a single electron, we can determine the number of electrons.
Total net charge of the system = -5.920 × 10^(-17) C
Charge of a single electron = -1.602 × 10^(-19) C
Number of electrons = Total net charge of the system / Charge of a single electron
Number of electrons = (-5.920 × 10^(-17) C) / (-1.602 × 10^(-19) C)
By simplifying the expression, we get:
Number of electrons = 36.93
Since we are looking for an exact number, we would round down the value to the nearest whole number. Therefore, there are exactly 36 electrons in this system.
B) The mass of the system can be calculated by summing the individual masses of the particles in the system. The mass of a proton is approximately 1.67 × 10^(-27) kg, and the mass of an electron is approximately 9.11 × 10^(-31) kg.
First, let's calculate the total mass contributed by the protons:
Number of protons = Total number of particles - Number of electrons
Number of protons = 1216 - 36 = 1180
Mass contributed by the protons = Number of protons * Mass of a proton
Mass contributed by the protons = (1180) * (1.67 × 10^(-27) kg)
Next, let's calculate the total mass contributed by the electrons:
Mass contributed by the electrons = Number of electrons * Mass of an electron
Mass contributed by the electrons = (36) * (9.11 × 10^(-31) kg)
Finally, let's calculate the total mass of the system:
Total mass of the system = Mass contributed by protons + Mass contributed by electrons
Total mass of the system = (mass contributed by the protons) + (mass contributed by the electrons)
To find the mass of the system, simply add the contributions from protons and electrons together. Round the result to three significant digits.
After calculating the values, we find that the mass of the system is approximately 1.96 × 10^(-24) kg.