The Regions of the Spectrum

Transcript

0:00Introduction

Hello everyone! Let me start with a small puzzle. Think of three things: radio waves carrying a cricket commentary, the light coming from this screen, and the X-rays a doctor uses to see a broken bone. Three completely different things, right? And yet all three are the same kind of wave: electromagnetic waves. So what makes them so different? Today we find out, region by region. Questions on this topic come up often in JEE, and they are quick marks. So, let's begin.

0:35One family of waves, one speed

So, here is the first part of the answer. Every electromagnetic wave, E M wave for short, travels at the same speed in vacuum: small c, the speed of light. Radio waves, light and X-rays all move at this same speed c, okay? Now look at the figure: seven regions side by side, from radio waves on the left to gamma rays on the right. If they all move at the same speed, what changes from one region to the next? Only the frequency, yes, exactly! We write frequency as nu, the Greek letter on screen that looks like a small v, okay? In the figure, the upper arrow is marked nu, in hertz, the H z at its end, and frequency increases to the right. Clear so far? Now, the wavelength, lambda, the Greek letter you see on screen, equals c over nu. And the energy of one photon, capital E, equals h times nu, where h is Planck's constant. So a higher frequency means a shorter wavelength and a bigger photon energy. That is why the lower arrow, marked lambda, points to the left. With me? There is one more thing in the figure: the regions merge into one another, with no sharp wall between them. The boundaries are conventional, just an agreement, so the edge values can differ from one book or figure to another, and even between this figure and the table that comes next.

2:00Long waves: wavelength; produced by; detected by

Okay? Alright, now the regions one by one, longest wavelength first, with the columns named in the heading. Radio waves have lambda greater than zero point one metre; the m on screen is metre. They are produced by oscillating charges in aerials, and detected by receiver aerials. Right? Next come microwaves, from zero point one metre down to one millimetre, the m m on screen. They are produced by a klystron or a magnetron, and detected by point-contact diodes. Got it? Below one millimetre comes the infrared, which runs down to seven hundred nanometres; n m is the nanometre. It is produced by vibrating atoms and molecules, and detected by a thermopile or a bolometer. Clear?

2:45Short waves: wavelength; produced by; detected by

Now the narrow band our eyes can see: visible light, from seven hundred nanometres down to four hundred nanometres. It is produced by electrons in atoms, and detected by the eye, a photocell, or film. Okay? Below four hundred nanometres, we enter the ultraviolet, which goes down to one nanometre. It comes from the inner electrons of atoms, and a photocell or film detects it. Right? Then come the X-rays, from one nanometre down to ten to the power minus three nanometre. They are produced in an X-ray tube, or when inner electrons of atoms jump to a lower level, and detected by film or a Geiger tube. With me? Only one region is left now, the one with the shortest wavelength of all. Which region is it? It is gamma rays, perfect! Their wavelength is less than ten to the power minus three nanometre; that sign is less than. They come from the radioactive decay of nuclei, and film or a Geiger tube detects them. Clear?

3:49Orders to remember

So, here is the whole spectrum in one line, by wavelength, from longest to shortest: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays. The sign between them is greater than. Okay? Now, frequency, photon energy and penetrating power go in exactly the reverse order. So gamma rays are the highest on all three, and radio waves the lowest. Got it? Now a question that catches many students. Gamma photons carry the most energy. So, in vacuum, do gamma rays travel faster than radio waves? They do not, so be careful here! In vacuum, every region travels at the same speed c, as you see on screen. More photon energy comes from a higher frequency, not from a higher speed. Right? Inside the visible band, red light, at about seven hundred nanometres, has the longest wavelength, and violet, at about four hundred nanometres, the shortest. The wavy equals sign means approximately. Clear? And here is a topper's trick for photon energy. E equals h times nu, which is h c over lambda. In handy units, E in electron volts, the e V on screen, equals one thousand two hundred and forty, over lambda in nanometres. You need no powers of ten at all. With me?

5:15Example 1: X-rays, UV, IR, microwaves by rising wavelength

Now, our first example, straight from the course. Arrange these in order of increasing wavelength: X-rays, microwaves, ultraviolet and infrared. Pause the video and try it first. Done? Okay, let's check. Many students write microwaves, infrared, ultraviolet, X-rays straight away, because that is the order we just learnt. So, is that the answer? No, that is the wrong way round, so be careful! Increasing wavelength means we start from the shortest. So, X-rays first, then ultraviolet, then infrared, and microwaves last, with the less than sign between them. Check it on the figure: wavelength increases to the left, so read from right to left. Got it?

6:03Example 2: name the region from a frequency or wavelength

Now a harder one, also from the course. Which region does each belong to? In part A, lambda is one centimetre, the c m on screen. In part B, nu is five times ten to the power fourteen hertz. In part C, nu is ten to the power eighteen hertz. And in part D, nu is three megahertz, the M H z on screen. Pause the video and try it first. Done? Okay, let's check. Our tool is lambda equals c over nu, with c equal to three times ten to the power eight metres per second, written on screen as m s to the power minus one. And remember, one nanometre is ten to the power minus nine metre. Okay? Part A is already a wavelength. One centimetre is zero point zero one metre, which lies between zero point one metre and one millimetre. The double arrow means implies, so it is a microwave. Right? For part B, lambda equals three times ten to the power eight, over five times ten to the power fourteen. That gives six times ten to the power minus seven metre, which is six hundred nanometres, inside the visible band. So it is visible light. Clear? Now part C, where nu is ten to the power eighteen hertz. Such a huge frequency, so it must be gamma rays, right? Before you answer, find the wavelength. It is not gamma rays, so careful here! Three times ten to the power eight, over ten to the power eighteen, gives three times ten to the power minus ten metre, or zero point three nanometre. That lies between one nanometre and ten to the power minus three nanometre, so these are X-rays. Always find the wavelength first. Got it? And for part D, three megahertz is three times ten to the power six hertz. Three times ten to the power eight, over three times ten to the power six, gives one hundred metres, far more than zero point one metre. So these are radio waves, very good!

8:09Quick revision: spectrum order and E in eV = 1240/lambda

So, quick revision. All E M waves travel at the same speed c in vacuum; only the frequency differs. By wavelength, longest first: radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays. Frequency and photon energy go the reverse way, and E in electron volts is one thousand two hundred and forty, over lambda in nanometres. Now go and try the practice problems on this page. All the best!