00:01
We're asked to find the wavelength of a hydrogen atom at room temperature.
00:04
So at room temperature, the temperature is about 300 kelvin, so that's t.
00:08
The mass of the hydrogen atom can be approximated as 1 .67 times 10 to the minus 27 kilograms.
00:14
So to find the wavelength, we need to first find the velocity, and we can do that from the kinetic energy.
00:20
So the kinetic energy says that k .e., classically, is 1⁄2 times the mass, times the velocity squared.
00:27
But because this has a temperature that is known, we can also find the kinetic energy from temperature.
00:35
This is three halves times the bolstmann constant, which we can call k sub b times the temperature t.
00:43
Rearranging to solve for velocity, we find that velocity is equal to the square root of three times the boltzman constant, k sub b, times the temperature t divided by the mass.
00:58
So now that we have an expression for the velocity, we can find the wavelength, because wavelength is equal to plank's constant h divided by momentum p, or momentum is mass times velocity.
01:09
So this is plink's constant h divided by the mass, and then this is also divided by the velocity, but our velocity expression is written above...