00:01
So for this problem, we are told to suppose that liquid nickel is undercool until homogeneous nucleation occurs.
00:10
So for part a of this problem, we are asked about the critical radius of the nucleus that is required.
00:25
So let's call this radius, the radius art.
00:30
So with that said, we know that this critical radius is.
00:35
Is defined as two times the solid liquid interface energy, the word conical sigma as out.
00:46
This times the temperature.
00:55
The temperature, that is, this is called the freezing temperature, and this divided by the product between the heat of fusion, and also the change in temperature.
01:12
Which is the typical undercooling for homogeneous nucleation.
01:18
So in this case, you need to find the values for nickel, which is the material or, yes, the element that we have in this case.
01:29
So the value for the freezing temperature, if you search for that value, is going to be 1 ,453 in this in celsius degrees.
01:43
Can pass this to kelvin by just adding to this value 274, and then we'll obtain this in kelvin.
01:51
And also, we can find the value of the solid liquid interface.
01:59
That value is going to be, let me see in here, is 255 times 10 to the minus 7 in units of joules per centimeter, square.
02:20
We are also, we can find the value of the heat of fusion and that heat of fusion for for nickel is equal to a value of 2 ,756 joules per cubic centimeter.
02:48
Finally, the last value that we can find for this is the typical undercullen for homogeneous nucleation, which is going to be a value of 480 celsius degrees.
03:12
So to this value, we just need to add 274 to pass this into kelvin.
03:21
So we substitute all of these values in here.
03:24
So we'll have 2 times sigma, which is 2.
03:31
255 times 10 to the minus 7 joules per cubic centimeter.
03:37
This times the freezing temperature, that is 1 ,453 plus 274.
03:47
So from there we obtain a value of 1 ,7277.
03:53
This divided by the heat of fusion, which is equal to 2 ,77...