00:02
Hello, here we have to solve the following problem.
00:06
An electron is a 1d box and when transition from n of 1 to n of 2 occurs, wavelengths of lambda 0, which is 426 nanometers, is emitted.
00:23
Now we have to determine, in question a, we have to determine the wavelengths, as lambda a, which corresponds to the transition from n of 2 to n of 3.
00:38
Before we do it, let's look at the initial transition from 1 to 2.
00:45
So here, en or energy of an reaction in 1d box equals to n squared times h squared over 8ml squared.
00:58
So therefore hc over lambda 0 equals to e2 minus e1 or that is 4 h squared over 8 m l squared minus h squared over 8 m l squared which is 3 eighth m 3 8x times h c oh sorry 3 eighth times h squared over m l squared.
01:36
And finally, from this equation, we will express hc or h squared over ml squared.
01:53
So that is 8 thirds of hc over lambda.
02:02
Let me write it more clear.
02:07
And that's an expression which we'll be using to answer questions and b so let's get back to our question a now transition from two to three occurs then hc over lambda a equals to nine h squared over 8m l squared minus 4 h squared over 8m l squared so that equals to 5h squared over 8 ml squared and that is then 5 eighths multiplied by 8 thirds hc over lambda 0 which is 5 thirds hc over lambda 0 then hc over lambda a equals to 5 thirds hc over lambda 0 and consequently lambda equals to 3 5th lambda 0 which is 0 .6 times 626 nanometers.
03:20
Let's complete this calculation.
03:24
That is 255 .6 nanometers.
03:28
That is roughly 256 nanometers.
03:32
Let's solve this problem.
03:35
Let's move on to the next question...