00:01
Hello students, in this question we have given that there are 10 to power 23 elementary dipoles in a two state paramagnet whose total energy is 0.
00:12
In the first part we have to find the number of accessible states which will be equal to n factorial divided by n divided by 2 factorial square.
00:38
Now, from sterling formula we can write n to power n, e to power minus n under root 2 pi l equal to n factorial.
00:53
We'll simplify this using this formula, so it will be n to power n to power n, e to power minus n under root 2 pi n, divided by n divided by 2, 2, 2 power, n divided, divided by 2, e to par minus n divided by 2, under root 2 pi n divided by 2, and this will be whole square.
01:27
Now from the denominator term will move out, will take out 1 divided by 2 and that 1 by 2 into 2 will be multiplied with 2 and it will be multiplied with 2 and it will well down to 1.
01:48
Let's write this n to par n to par n to par minus n, the root to pi n divided by n divided by 2 to the power n to par n to par minus n this will be pi n this will be 2 multiplied by 1 by 2 so this will be 1.
02:17
Now we'll be left with 2 to power n in under root we will have 2 divided by pi n.
02:33
If we will put the value n equals to 10 to par 23, we'll get pi as 2 to the power 10 to the power 203 into 5 is 2 to the power 10 to the power 23 into or multiplied by 2 divided by pi to power 23 this will boil down to 2 to power 10 to power 23 multiplied by 2 .5 to multiplied by 10 to power minus 12 so this will be the number of accessible states now in the second part we have given that that this system changes a billion states per second so it changes billion states per second.
03:37
This will be equal to 10 to power 9 states per second.
03:46
Now in 10 billion years, first of all simplify this into seconds...