Some Typical Kinetic Energies. (a) In the Bohr model of the...

Some Typical Kinetic Energies. (a) In the Bohr model of the atom, the ground-state electron in hydrogen has an orbital speed of 2190 $\mathrm{km} / \mathrm{s} .$ What is its kinetic energy? (Consult Appendix F.) (b) If you drop a 1.0-kg weight (about 2 lb) from a height of 1.0 $\mathrm{m}$ , how many joules of kinetic energy will it have when it reaches the ground? (c) Is it reasonable that a $30-\mathrm{kg}$ child could run fast enough to have 100 $\mathrm{J}$ of kinetic energy?

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It is defined as one-half of the object's mass multiplied by the square of its velocity (KE = 1/2 m v²). This concept is fundamental in classical mechanics and is applicable across scales, from subatomic particles to large macroscopic objects, providing insight into energy transformations during motion.

Bohr Model of the Atom

The Bohr model describes atoms as having electrons that orbit the nucleus in fixed, quantized orbits, each associated with a specific energy level. This model incorporates early quantum ideas and allows for calculations of electron properties, such as orbital speed and kinetic energy, by considering the quantization of angular momentum and energy levels.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position within a gravitational field, typically calculated as the product of mass, gravitational acceleration, and height (PE = mgh). This energy converts into kinetic energy as the object falls, illustrating the conservation of energy in macroscopic systems.

Energy Scales in Different Contexts

Understanding energy scales involves comparing the magnitudes of energy in various systems, such as the low kinetic energy of everyday movements versus the extremely high energies associated with subatomic particles. This concept is critical for evaluating the plausibility of energy estimates and ensuring that calculations make sense within the context of the physical system being analyzed.

Transcript

00:01 Hello, hi.

00:03 Once again, we have a new problem, and this time it's a model, it's a ball model, and it's an atom with a ground state electron.

00:18 Okay, ground state electron looking at kinetic energy.

00:23 So this is a hydrogen atom.

00:29 So it's a hydrogen atom.

00:33 And the orbital.

00:36 Speed happens to be 2 ,190 kilometers per second, which is the same as 2190 times 10 to the 3 meters per second.

00:50 And also the mass of the electron happens to be 9 .11 times 10 to the negative 31 kilograms.

01:00 So the first part of the problem is to find the kinetic energy, which is given by 1 .5 mv squared.

01:07 We substitute those numbers so the mass is 9 .1 times 10 to the negative 31 kilograms and then you multiply that by the velocity which is 2190 times 10 to the 3 meters per second so we're using the kinetic energy formula which is the energy that the electron has while moving and so if you plug in the numbers in your calculator you get 2 .1a times 10 to the 18 joules.

01:43 And that's the kinetic energy of the electron.

01:52 It's in orbital speed, meaning it's rotating.

01:57 On the second page, we have the second part of the problem.

02:01 But b, and this time we are going to have kind of like a different problem, where you have a weight happens to be 1 kilogram, 1 .0 kilograms, which is approximately 2 pounds, and you're dropping it to a height h, which is 1 meter.

02:27 Okay? so we want to find the jewels in kinetic energy it's going to have when it hits the ground.

02:35 So this is the ground.

02:35 Remember, there's an energy transformation going on from potential energy up until kinetic energy, by the law of conservation of energy, will say kinetic energy of the object equals to mgh.

02:51 So this just means that all the energy, we don't have any losses.

02:56 So this is the same as one kilogram times 9 .8 meters per second squared times 1 .0 meters.

03:07 If you plug in those numbers, you get 9 .8 joules.

03:11 So this is the conversion.

03:13 There is a conversion of potential energy to kinetic energy.

03:22 And so on the ground, that's going to be the kinetic energy when it reaches the ground.

03:28 In the third page, we have, let's just see, this, yeah, 9 .8 joules...

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