AIEEE and Earlier JEE Main Questions: Spectrum

Transcript

0:00Introduction

Hello everyone! Let me start with a small puzzle. Cosmic rays, gamma rays, beta rays and X-rays. All four have the same last name, rays. So, are all four of them electromagnetic waves, like light? Hmm, careful here, because the word rays can fool you. We will settle this in example one. Today we solve past JEE questions on the electromagnetic spectrum, from A I triple E and the earlier JEE Main papers. Questions like these come up often, and they are quick marks once you know the spectrum well. So, let's begin.

0:38One family, one speed

So, first, look at the figure. This is the electromagnetic spectrum, seven regions in one strip: radio waves on the left, then microwaves, infrared, visible light, ultraviolet and X-rays, and gamma rays on the right. The top arrow is nu, the Greek letter for frequency, measured in hertz, the H z on screen; it increases to the right. The lower arrow is lambda, the Greek letter for wavelength, and it increases to the left, just as the red note at the bottom says. With me? Now, radio waves sit at one end, and gamma rays at the other end. Completely different, right? But one thing is exactly the same for both of them in vacuum. What is it? It is the speed, yes, exactly! All electromagnetic waves travel at the same speed in vacuum, c, the speed of light. They differ only in their frequency, nu. Okay? And the frequency fixes everything else. Lambda equals c over nu, so a higher frequency means a shorter wavelength. And the energy of one photon, capital E, equals h times nu, where h is Planck's constant. So a higher frequency also means more energy in each photon. Right? Now, one more thing about this figure. The numbers along the two arrows, powers of ten in hertz on top, and metres, millimetres and nanometres below, are only rough boundaries. The regions merge into one another, so the boundaries are conventional: agreed upon, not sharp. Clear?

2:10Orders to remember

Now, the orders. Questions on them come up often, so let us build them together. Tell me, which region has the longest wavelength? It is radio waves, that is correct! Then the wavelength keeps falling: radio, microwave, infrared, visible, ultraviolet, X-rays, and gamma rays the shortest. The greater-than sign means longer than, and U V on screen is short for ultraviolet. Okay? Now, which region carries the most energy in each photon? It is gamma rays, yes, exactly! Frequency, photon energy and penetrating power all go in the reverse order. Shortest wavelength, highest frequency, biggest photon energy, and the most penetrating. With me? Inside visible light also, there is an order. Red, at about seven hundred nanometres, has the longest wavelength, and violet, at about four hundred nanometres, has the shortest. The wavy equals sign means about, and n m is the nanometre. Got it? And here is a topper's trick from the course. Photon energy in electron volts, the e V in brackets, equals one thousand two hundred and forty, over the wavelength in nanometres. So for a five hundred nanometre photon, one thousand two hundred and forty over five hundred gives two point four eight electron volts. See how quick that is?

3:35Who produces it, and who detects it

Next, the course table also tells us what produces each region, and what detects it. The arrow on screen means detected by. Microwaves are produced by a klystron or a magnetron, and detected by point-contact diodes. Okay? Infrared comes from vibrating atoms and molecules, and is detected by a thermopile or a bolometer. Right? X-rays come from an X-ray tube, from the inner electrons of atoms, and we detect them with photographic film or a Geiger tube. With me? And gamma rays come from the radioactive decay of nuclei; again, film or a Geiger tube detects them. Clear? Now a quick past question, from A I triple E two thousand and two. Which instrument detects infrared radiation: a spectrometer, a pyrometer, a nanometer, or a photometer? The answer is the pyrometer, yes! Our table named the thermopile and the bolometer, but neither of them is among the options this time. And did you notice the trap? The nanometer is not an instrument at all; it is a unit of length, the same n m we use for wavelengths. Got it?

4:45Example 1: cosmic, gamma, beta or X-rays: which is not EM?

Now, example one, and it is our puzzle from the start. From A I triple E two thousand and two: which of these are not electromagnetic waves: cosmic rays, gamma rays, beta rays, or X-rays? Pause the video and try it first. Done? Okay, let's check. Some students say: all four are called rays, so all four must be electromagnetic waves, E M waves for short, right? Is that correct? No, no, careful, the name can fool you! Look at the figure: gamma rays and X-rays are the last two regions on the right, so they are electromagnetic waves. Okay? But beta rays are streams of electrons. So they are not electromagnetic waves, and you will not find them anywhere on this strip. Right? So the answer is beta rays. Puzzle solved: do not go by the name rays; always ask what the thing really is. Clear? One honest note before we move on. Cosmic rays are not a region of this strip either; they are mostly very fast protons and other nuclei, which are charged particles. Still, the expected answer to this question is beta rays, because beta rays are plainly streams of electrons. So in the exam, mark beta rays. Okay?

6:02Example 2: rank radio, yellow, blue, X-rays by photon energy

Now a harder one, example two, from JEE Main twenty sixteen. Arrange in order of increasing energy per quantum: blue light, called A, yellow light, called B, X-rays, called C, and radio waves, called D, okay? Pause the video and try it first. Done? Okay, let's check. One quantum means one photon, one packet of energy. Its energy is E equals h times nu, so the energy rises with frequency. Okay? Now, radio waves have the longest wavelength of all four. So radio waves carry the most energy per quantum, right? No, no, wait, it is the opposite! Longest wavelength means lowest frequency, so radio waves have the least energy. And X-rays, near the high frequency end of the figure, have the most energy of these four. With me? Now the two colours. Blue light or yellow light: which one has the higher frequency? It is blue, that is correct! In the rainbow order, blue lies nearer violet, the short wavelength end, and yellow lies nearer red. So blue has the shorter wavelength, the higher frequency, and more energy per photon. Right? So the order is D, then B, then A, then C: radio waves, yellow light, blue light, X-rays. The less-than sign means less energy than. If you wrote it the other way round, you ranked them by wavelength, so always check which quantity the question asks for, okay?

7:40Quick revision: same speed c, spectrum order, E = h nu

So, quick revision. All electromagnetic waves have the same speed c in vacuum; only the frequency and the wavelength differ. Wavelength falls from radio waves to gamma rays, while the frequency and the photon energy, h times nu, rise. And know the source and the detector of each region; beta rays are streams of electrons, not E M waves. Now go and try the practice problems on this page. All the best!