Overview

Transcript

0:00Introduction

Hello everyone! Okay, one quick situation before we start. In a helium ion, the electron falls from level three to level one, and out comes a photon. That photon now hits a hydrogen atom, sitting in its ground state. What happens to the hydrogen electron? Does it just jump to a higher level, or does it fly out of the atom completely? And with how much energy? Hmm, hold on to your answer. Today is a special lesson. You have finished Chapters one to eight of atomic structure, and now it is time to test yourself with the unit problem bank. I will show you how to use it like a real JEE paper, and we will solve this exact question together. So, let's begin.

0:43How to use this chapter

So, first of all, when should you open this chapter? After Chapters one to eight, okay? And Part A, at JEE Main level, you attempt as a forty minute test, with a clock, exactly like the exam. Part A has twenty problems. Twenty problems, forty minutes. So how much time can you give each one? Forty divided by twenty: two minutes a problem, that's it! Read it, spot the idea, write the answer. Stay fully focused. Then Part B, at JEE Advanced level, with longer problems. What makes them advanced? We will open that up in just a minute. And Part C checks the statements most often tested in true or false, or assertion and reason form. Short statements, but every word matters. Now, the trap. Many students see Part C and think, oh, no numbers, no calculation, I will just skip it, right? No, no, careful! These are exactly the statements examiners test most often, and one changed word can turn a true statement false. So read every word slowly, okay? And last, the unit test at the end. It has answers only, no worked solutions to peep at. So it is an honest test of you. Clear?

1:57Part B: what makes it Advanced?

Now, about Part B, okay? Tell me, what makes a problem JEE Advanced level? Bigger numbers? Longer calculations? Not really! Two or more ideas, joined in one problem. That is the secret. Each idea alone is easy for you now. The real skill is spotting where one idea ends and the next one begins. For example, spectra, plus the photoelectric effect: light made by one atom, knocking out electrons somewhere else. Keep this pair in mind, because our Example two is built just like it. Next, Bohr orbits, plus de Broglie waves: an electron going round an orbit, treated as a wave. And nodes, plus wave functions: finding a node straight from the formula of the wave function. Two ideas, one question.

2:44Two tools for the whole chapter

Got it? The chapter itself hands you two tools. Tool one, for photons: E in electron volts equals twelve forty over lambda in nanometres. Lambda, the Greek letter, is the wavelength, and the brackets just tell you the units, okay? Tool two, for energy levels. E sub n, that is E with a small n below, the energy of level n, equals minus thirteen point six, times Z squared over n squared, in electron volts. Small n is the level number, and capital Z is the nuclear charge. For hydrogen, this is simple. But in Part B you meet the helium ion again and again: H e plus, the little plus on top showing its charge. So what changes in this formula for H e plus? Only Z, that's right! For hydrogen, Z is one. For the helium ion, Z is two, so Z squared is four. So every level of H e plus is four times as deep as the same level of hydrogen. Remember this, it will save you in Example two.

3:45Example 1: energy of the n = 4 level of hydrogen

Alright, first a problem from Part A, an easy one. Find the energy of the electron in the n equals four level of hydrogen. Pause the video and try it. Your two minutes start now. Done? Okay, let's check. n is four, so minus thirteen point six divided by four: minus three point four electron volts, right? No, no, careful! Look at tool two again: it is n squared, not n, okay? For hydrogen, Z is one, so the Z squared part changes nothing. And n is four, so n squared is sixteen. So E four, that is E with a small four below, equals minus thirteen point six over sixteen: minus zero point eight five electron volts. And keep that minus sign; dropping it is a very common slip. One line, well inside your two minutes. With me?

4:42Example 2: He+ photon ejects a hydrogen electron

Now, our puzzle from the start. It is a Part B problem, JEE Advanced level. The photon emitted when the electron of H e plus falls from n equals three to n equals one strikes a hydrogen atom in its ground state. Find the kinetic energy of the electron ejected. Pause the video, and try it. Done? Okay, let's check. First, the photon. The electron falls from three to one, so its energy is thirteen point six, times one minus one ninth, right? No, no, careful! This is H e plus, not hydrogen. Remember tool two: Z is two, so Z squared is four. So thirteen point six becomes thirteen point six times four: fifty four point four electron volts. Forget Z squared here, and every number after this goes wrong. Now the jump from three to one. One over n squared is one for level one, and one ninth for level three. So the photon is fifty four point four, times one minus one ninth: about forty eight point four electron volts. The wavy equals sign means approximately, okay? Now the second idea. This photon hits a hydrogen atom in its ground state. So, remember our puzzle: does the electron just jump up, or does it fly out? It flies out, exactly! Removing the electron from ground-state hydrogen takes just thirteen point six electron volts, and our photon brings forty eight point four. Much more than enough. Whatever is left over becomes capital K, the kinetic energy of the ejected electron. Forty eight point four minus thirteen point six: about thirty four point eight electron volts. See? Our puzzle from the start, solved! One spectral line of the helium ion, joined with freeing a hydrogen electron: two ideas in one problem. That is exactly the Part B style. Clear?

6:44Quick revision: test plan, photon and level energy formulas

So, quick revision. Part A is a forty minute test, two minutes a problem, and Part B joins two or more ideas in one problem. For photons, twelve forty over lambda in nanometres gives electron volts; for levels, minus thirteen point six, times Z squared over n squared. Square n, square Z, which is four for the helium ion, and keep the minus sign. Now open Part A, start your clock, and begin. Then take the unit test at the end. You did the hard work in eight chapters, and this is where it pays off. All the best!