The mass of a helium atom is roughly four times that of a hydrogen atom. The mass of an oxygen atom is roughly 16 times that of a hydrogen atom.
a. For each of the following pairs, choose the one that has the greater kinetic energy: (i) a H atom moving at 1000 m/s or a He atom moving at 400 m/s, (ii) a H atom moving at 1000 m/s or an O atom moving at 400 m/s, (iii) a He atom moving at 1000 m/s or an O atom moving at 400 m/s.
b. A He atom is moving at 800 m/s. What is the speed of an O atom that has the same kinetic energy as the He atom?

Question

The mass of a helium atom is roughly four times that of a hydrogen atom. The mass of an oxygen atom is roughly 16 times that of a hydrogen atom.

a. For each of the following pairs, choose the one that has the greater kinetic energy: (i) a H atom moving at 1000 m/s or a He atom moving at 400 m/s, (ii) a H atom moving at 1000 m/s or an O atom moving at 400 m/s, (iii) a He atom moving at 1000 m/s or an O atom moving at 400 m/s.

b. A He atom is moving at 800 m/s. What is the speed of an O atom that has the same kinetic energy as the He atom?

Accepted Answer

welcome back everyone which of the following has a higher amount of kinetic energy. A tennis ball with a mass of 0.0 61 kg and a speed of 145 kilometers per hour or a tractor with a mass of 1750 kg and a speed of 25 kilometers per hour. So our first step is to recall our formula for calculating kinetic energy. We would recall that is represented by E sub K, which is equal to one half times the mass of our object times its velocity which is squared. So V here is again velocity and it should be in units of meters per second. Now our units for our kinetic energy should be in units of jewels. So let's go ahead and calculate the kinetic energy for our tennis ball 1st based on our formula. So we'll put an equal sign and we'll say that this is equal to one half times its mass given in the prompt as 0.61 kg. Multiplied by its velocity. Given in the prompt as 145 kilometers per hour. Where again we need to get our velocity in meters per second. So we're going to multiply to cancel out kilometers by recalling our conversion factor to go from kilometers into meters where our prefix kilo tells us that we have 10 to the third power of our base unit meters, canceling out kilometers. We're now going to get rid of our unit hours. Where we would recall that first we have In our numerator numerator are term hours. So one hour we would recall has an equivalent of 60 minutes. And now canceling out minutes. We're going to recall that we have In our numerator in equivalence of one minute to 60 seconds. And so now we can get rid of ours as well as minutes, leaving us with our final units of meters per second for velocity. And so simplifying everything when we take the product we're going to get a value of And sorry, we need to make sure we have that square power there from our formula. So be sure to include that in your calculations. And we would be able to simplify 49.5 and we're going to just to be clear place this unit here in brackets when we type this into our calculator so that we can have everything come out correctly. So what we can see is that we were left with units of kilograms times meters squared divided by second squared. Since we have this square power here. And so we have kilograms again, times meters squared divided by seconds squared. Where we want to recall that one jewel is actually equivalent to one kg times meter square divided by seconds squared. So we can actually interpret this answer as 49.5 jewels. So now we want to compare this calculation for our kinetic energy of the tennis ball to the tractor. So following the same process, we have the kinetic energy of our tractor equal to one half times the mass of the tractor given in the prompt as 1750 kg being multiplied in brackets by our velocity of our chapter given in the prompt as 25 kilometers per hour. Where again we want to get rid of the kilometer unit. So in our denominator recall that one kilometer has an equivalent of 10 to the third power meters. So now canceling out kilometers, we go from canceling out the unit hours in the numerator, which we would recall one hour is equal to 60 minutes, canceling out hours and now focusing on getting rid of minutes. We plug in one minute in the numerator which has an equivalent of 60 seconds. And so now we can cancel out minutes were left with meters per second. Again outside of our bracket we have our square power which is being applied to our units of meters and seconds. And so taking the product of everything we're going to get that are kinetic energy of our chapter is equal to 42,197 0.1 jewels. Which and sorry not jewels yet because as we stated, we have kilograms times meters squared divided by seconds squared, which yes, we can interpret as 42,197 0.1 jewels. However, we want to write this in scientific notation, 2366 and so We're going to write this to about 4.22 times 10 to the 4th power Jules. And this would be since it's a power of 10 to the four versus our first calculation for the kinetic energy being just 49.5, we're going to consider the kinetic energy of our tractor as the higher kinetic energy. And so we would complete this example by saying that the tractor has a higher kinetic energy. And so this statement would be our final answer to complete this example. I hope that everything I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

Verified Solution

Key Concepts

Kinetic Energy

Mass and Velocity Relationship

Conservation of Energy