STUDIES I N T H E EXPERIMEKTAL TECHKIQUE O F PHOTOCHEMISTRY
11. T H E DETERMINATION O F T H E ENERGY DISTRIBUTIOX AXD T H E TOTAL ENERGY I X T H E RADIATIOK FROM QUARTZ MERCURY VAPOUR LAMPS BY R . G. FRANKLIN, R. E. W. MADDISON AND L. REEVE
In the first paper of this series1 it was pointed out that, for the complete investigation of a photochemical reaction, it was necessary to determine the so-called “energy characteristics” of the light source employed; i. e., the total energy in the beam of light from it (expressed as ergs per sq. cm. per second) together with the distribution of this energy amongst the various wave lengths comprising the lamp’s radiation. h brief account was also given of the methods employed for determining these energy characteristics. It is proposed, in the following paper, to describe these methods more fully, with particular reference to the light source most commonly employed by photochemists, viz: the quartz mercury vapour lamp. The determination of the energy distribution will be considered first. Determination of Energy Distribution
A. Apparatus employed. As mentioned in the last paper, the method employed in this laboratory for determining energy distribution is the direct one, using a spectrometer, spectro-thermopile and galvanometer. The disposition of the complete apparatus is shown in Fig. I , a detailed description of which mill now be given, under the following headings :T h e Spectrometer and Linear Thermopile. The spectrometer F is a Hilger monochromatic illuminator for the ultra violet and is fitted with quartz telescope and collimator lenses, a quartz prism and a metallic mirror. The collimator and telescope slits are fitted with micrometer adjustments each division on which corresponds to 0.001 inches ( 0 . 0 2 5 mms.). To the eyepiece end of the telescope tube is fitted a brass block, in a receptacle in which is a Kilger linear thermopile L of resistance about I O ohms. This block was found to be an insufficient protection against draughts, which set up thermoelectric potentials greater than those given by niany of the lines in the mercury spectrum. The block and thermopile have therefore been enclosed in a wooden box, painted dull black inside, covered outside with aluminium foil and packed vith cotton wool. Through a small hole in one side pass the galvanometer leads. J. Phys. Chem. 29, 39 (1925’.
7=4
R. G. FRANKLIN, R. E. TV. JIADDISOE AND L. REEVE
Another similar wooden box, but without cotton wool, is fitted over the prism table of the instrument. Both boxes are shown dotted in Fig. I . The whole front of the instrument is protected froin the heating effect of the lamps used, by means of a hollow, water-cooled, copper screen M, about 2 5 cms. square. A rectangular aperture about 3 cms. by 1.5 cms. is cut through this, exactly in front of the collimator slit. This aperture is normally covered by a smaller, hollow, water-cooled screen, about T O cms. square, which the operator can raise by pulling a suitably arranged cord.
The Galzianometer G. This is a moving magnet instrument of the Paschen type, the suspended system of which is extremely light. The internal resistance of its four coils, arranged in series parallel, is 11.77 ohms. Its sensitivity can be varied from
FIG.I
about 80 to 400 mms. per microvolt a t I metre by means of an external controlling magnet, whilst its period, when shielded, varies from 2 to 6 seconds according to the sensitivity. Deflection and current are proportional. The instrument is protected against external magnetic fluctuations by means of two massive dome shaped shields of a special steel. The thermopile leads are connected directly to the galvanometer, as it was found that switches introduced varying thermoelectric and contact E. M. F. s. The unavoidable junctions a t the terminals are heavily lagged with cotton wool and, t o avoid draughts, the whole inside of the galvanometer, wherever possible, is protected in the same manner. The galvanometer is used in a laboratory in the basement of the building and stands on a stoutly built wooden table resting on a concrete bed sunk into the floor. Despite all these precautions, no greater steadiness of zero than 3 mms. on maximum sensitivity can be attained under average conditions. The biggest disturbing factor is the too close proximity of electrical machinery, particularly of electric tramways about I O O yards away. Some of the more spasmodic deflections have been traced to the opening and closing of the laboratory door: others, however, are still inexplicable. Apart from these spasmodic deflections, trouble is experienced through a steady creep of the zero across the scale. This is probably due to a steady heating up of one side of the thermopile. It has to
EXPERIMESTAL TECHNIQUE O F PHOTO CHEMISTRY
715
be constantly corrected by an appropriate movement of the controlling magnet. Unfortunately this alters the sensitivity of the instrument, which, therefore, has to be redetermined each time the zero is brought back.
The Standardising Cod H . This is done by passing a known current of about 0.1ampere through the standardisinp coil H, a method due to Coblentz'. The coil is about I j cms. in diameter and consists of an appropriate number of turns of mire mounted on the galvanometer table a few inches in front of the outer shield of the instrument and in a plane parallel to its coils. It is standardised by first connecting the galvanometer directly to the output leads of a potentiometer which, when its input leads are connected to an accumulator cell, gives a P. D. of just over I microvolt. The deflection per microvolt is thus determined. The standardising coil circuit is then closed and the deflection given by the palvanometer observed. By variation of a resistance S in series with the coil, the current through it is coiitrolled until the deflection obtained is equal to that given by the microvolt P. D. applied directly a t the terminals of the instrument. The sendiivity of any subsequent occasion can be determined by passing the same current through the standardising coil; and, since the coil circuit is entirely external t o the galvanometer, errors which would be introduced by change-over switches in the thermopile circuit are entirely avoided. I n recording galvanometer deflections, readings are generally reduced to a standard sensitivity of z 5 0 mms. per microvolt. The Mounting of the Lnmps. The mercury lamps used are mounted on brass frameworks on wooden stands screwed to the steel slides of an optical bench. Immediately in front of the lamp A and extending over its whole width is fixed an aluminium framework carrying an aluminium diaphragm B pierced with a suitable-sized circular aperture. Three interchangeable diaphragms are used with apertures I .o, I . 2 and I .4 cnis. in diameter respectively. These diaphragms are arranged to lie in the focal plane of a quartz condenser lens C, of 7.6 cms. available aperture and 1 o . j ems. focal length. The approximately parallel beam of light thus produced, sifter passing through a I em. deep water-cell with quartz sides E and any other necessary light filters, is used in all the quantitative photochemical work for which the lamp is required. For energy distribution determinations another quartz lens D is utilized, arranged to refocus the parallel beam onto the collimator slit of the spectrometer when the shutter covering it is raised. B. Method of taking Ubservationz. The wave-length drum of the spectrometer is set to its lowest reading, and collimator and telescope lenses are adjusted t o be in focus for this wave length. The shutter covering the collimator slit is then raised and the galvanometer deflection observed. This procedure is carried out till the whole of the spectrum has been worked through. -
'Bull. Bur. Standards 9, 33 (1911).
716
R. G . FRANKLIS, R. E. W. MADDISOR- AND L . R E E V E
Rlention has already been made of the unsteadiness of the Paschen galvanometer. Hence, in order to obtain an accurate value for the deflection a t any point the following method has been finally adopted. One observer takes a series of readings for the deflection produced by a spectral line and for the sensitivity as given by the standardising coil. Any readings which show a sudden change in the rate of swing as the spot passes across the scale are rejected. In this way between five and twenty fairly concordant readings are obtained. Another observer does likewise. If both sets of readings give the same mean value, this is taken as a trustworthy result. If not, the whole operation i s repeated. It follows that each galvanometer deflection recorded represents the mean of from ten to forty separate observations.
FIG.za
t
FIG.zb
C . The Representation of the Results. The results obtaincd for a given lamp are represented graphically by plotting the galvanometer deflections (reduced to a standard sensitivity) against the wave length. Such a curve was shown in Fig. I of the first paper in this series'. It was shown in that paper that the true energy distribution between the spectral lines, whether they be simple or compound, could be obtained from the areas of the triangular diagrams which they give, if these are divided by the corresponding values of dX, the wave length range embraced by the telescope slit at that part of the spectrum. A more detailed discussion of this matter, particularly of the relation between the nature of the line and the shape of the triangular diagram it gives, was also promised. It is proposed to give this here. It will be remembered that a pure spectral line is nothing but an image in monochromatic light of the collimator slit and, owing to the symmetry of the optical system of the spectrometer, of exactly the same size. If a line is comReeve: J. Phys. Chem. 2Q, 40 (1925).
EXPERIMENTAL T E CHSIQUE O F PHOTOCHEMISTRY
717
pound it will give a number of images, each the size of the collimator slit, which images may or may not overlap, according to the wave length difference dX between the components. I n every case, however, the base of the triangular diagram, expressed as a wave length range, is equal to the sum of the wave length ranges embraced by the width of the telescope slit and the width of the spectral line respectively. Remembering these points, let us now go on to consider the possible values of the width of this base, and the possible shapes of the graph figures. Case I. Pure 1>znes. ( a ) Collimator and Telescope Slits of Same Width. (say I O divisions). The graph figure will be a practically isosceles triangle of base 2dX and height x (the maximum galvanometer deflection). See Fig. 2a. dX is the wave length range embraced by a telescope slit of I O divisions. Area of Fig. 2a = x.dX; divide by dX; = result = x. It is obvious that, if all the lines were pure, the relative energy distribution between them would be given by the respective values of x. Some of the lines are compound, however, and this introduces complications which mill be dealt with in due course. Meanwhile the above procedure sliould be noted. '
+%PA
( b ) Telescope Slit wider than Collimator Slit. (say collimator slit of I O and telescope slit of 1 2 divisions.) The effect of this inequality is to continue the maximum deflection x through a wave length range equal to the FIG.Z c difference between the two slit widths. See Fig. 2b. Area of figure = (1.2x)dX; divide by dX; result = 1 . 2 ~ . It is again obvious that if all the lines mere pure their relative energy would be given by the values of x. Case 11. Compound Lmes. It will now be shown that the diagram given by a compound line is due to the sum of the diagrams given by the separate components, and hence its energy is still obtainable by dividing the area by the mean dX for the line. Assume for the sake of simplicity that we are dealing with a compound line made up of two components X and X'of equal intensity, each of which alone would have given a maximum galvanometer dejfection of x. Let X - A ' = dX. Then, a$ we have already mentioned, the spectral line will consist of two images, each in monochromatic light, of the collimator slit, which may or may not overlap, depending upon the relative values of aX and dX.
( a ) Slits of Equal Width. Again, let us first consider the case of equal slits, say again Case I . dX < dX
IO
divisions.
718
R. G . FRASKLIX, R . E. W. M A D D I S O S A N D L. REEVE
The images of' the two components will overlap as shown in Fig. zc. The total width of the line is dX dX.
+
The line is made up of three portions:( I ) A central portion, width dX - dX; Le., less than the width of the telescope slit by ah. This portion by itself, when fully embraced by the telescope dX - dX slit would, therefore, give a deflection of ___ zx dX ( 2 ) Portions on each side of this of width dX, each of which alone, would be
ah
responsible for a maximum deflection of -x. Hence, as the compound line dX moves across the slit, it will be responsible for galvanometer deflections expressing themselves in a diagram of the type shown in Fig. z d . This can be
1 2
FIG.zf
3 4
56
FIG.2d
seen more clearly by considering Fig. ze, in which the dotted lines represent the two spectral images of the components, and the full line represents the telescope slit. Assuming a movement of the lines across the slit froin left to right, the figure shows the relative position of the two images and the slit for the six limiting galvanometer deflections marked I to 6 in Fig. 2d; e.g., at the position of the lines and slit shown by 2 , Fig. 2 8 , the deflection obtained is given by the ordinate a t the point 2 of the graph diagram Fig. 2d: at position 3 of Fig. 2 0 the deflection is given by the ordinate at point 3 of Fig. 2d and so on; whilst at intermediate positions we have intermediate deflections.
+
The total width of the base of the graph diagram Fig. zd is 2dX ah; the excess above that given.bya pure line is therefore dX which is equal to the wave length difference between the components. Fee the first paper of this series'. 1
Reeve: J. Phys. Chem. 2 9 , 41 (1925).
EXPERIMESTAL TECHNIQUE O F PHOTO CHEMISTRY
719
The area of the diagram can easily be shown' t o be 2x.dX. Divide by dX. Result = zx; i. e., the same result as would have been obtained had the two lines registered their effects separately. (Xote however that the maximum deflection obtained is less than 2x.). This additive property of the diagram is of course also true graphically; add up two triangles each of base 2 dX and height 5 , separated by a distance 8X less than dX, as shown in Fig. z f , and Fig. zd will be obtained.
FIG.2e
Case 2. = dX For all values of dX up to dX similar diagrams as for Case I would be obtained. When dX = dX the images of the two components would just touch; see Fig. 3a. The result on the energy distribution diagram would therefore be as shown in Fig. 3b. Area of this is zdX.x; divide by dX; result = zx,the same result as would have been obtained had the two components registered their zffects separately. Also, it is again true graphically; see Fig. 3c.
FIG.3a
Case 3 . dX > dX but < zdX If now becomes greater than dh (but less than 2dX) the images of the two components separate, the distance between them being dX - dX. The result on the energy distribution diagram is shown in Fig. 3d, where a = dX, b = dX - dX, c = 2dX - ah, and, therefore, b c = dX.
+
Area of portion 3 4 =
The sum of all which
ai =
zx. dX
720
R. G. FRANKLIK, R. E. W-,MADDISON AND L. REEVE
The limiting positions of the telescope slit and the spectral images are shown in Fig. je, using the same method of presentation as described under Case I , Fig. 2 8 . The area of Fig. 3d can again be shown to be equal to 2dX.x; divide by dX and the result is zx: again the same result as would have been given by the sum of the two separate components. An inspection of the diagram will show that this is also true graphically.
1
2.3
4 5
6
FIG.gd
Case 4. ah = 2dX The images are now separated by a distance equivalent to dX. The result is that they are just resolved by the spectrometer, see Fig. 4a, the area of which is once again 2dX.x. Divide by dX and we get the usual result, 2x. Case 5 . aX > 2dX The components are now two completely separable lines, as shown in Fig. 4b.
FIG.3e
Effect of Inequality of Intensity of Components. I n the above discussion we have been assuming the components to be of equal intensity. The general effect of an inequality would be t o make all the above symmetrical diagrams asymmetrical. Thus, any horizontal portions of the diagrams would now slope up or down, according to whether the left hand or the right hand component mer6 the inore intense. If the components separately were capable of giving maximum deflections of x and y respectively then, on dividing the area of the complex diagram by the mean dX for the lines, the result would be x y. For, as me have shown already for a number of cases, the compound energy distribution diagram is the sum of the simpler triangular
+
EXPERIMENTAL TE CHKIQUE O F PHOTO CHEMISTRY
721
diagrams due to the separate components. The areas of these, divided by their respective dX’s give the results x and y respectively; Hence, on doing this with the compound diagram, the result would be x y.
+
( b ) Slits of Cnequal Width. E. g. telescope slit of 1 2 divisions and collimator slit of I O . In the case of a simple line, it will be remembered, the effect of inequality in slits was to introduce a phase of constant deflection into the graph diagram, so that instead of a triangle we obtained a trapezium. On dividing the area of this figure by dX we obtained the result 1.2x instead of x. This factor 1.2 would enter into all other pure lines; hence the relative energy of these would remain unaffected. Turning now to compound lines: the effect of a wider telescope
FIG.4a
FIG.4b
slit on the diagram given by these would be t o introduce extra phases into the energy distribution diagram. Thus with equal slits Case I , where ax < dX, gave the diagram shown in Fig. 2d. With a wider telescope slit this would now appear as shown in Fig. 4c. the limiting positions of slit and lines for which, numbered in the usual manner, are given in Fig. 4d. The slope of the side of a graph diagram may be taken as a measure of the rate of increase or decrease in intensity of the radiation falling upon the thermopile. Hence any sudden change of slope is due to a sudden change in this rate. Referring now to Fig. 4c, from I t o 2 the rate of increase is due t o an increasing amount of one component passing through the telescope slit. From 2 to 3 the rate is doubled since both components are now acting. From 3 to 4, although deflections are still increasing, they do so a t the same rate as for the section I t o 2 ; for the increasing deflection is due to the telescope slit embracing an increasing portion of one component only. From 4 to j the deflection remains constant, i. e., the rate of increase is zero. For, although the right hand edge of the right hand component is passing off the slit, exactly equivalent portions of the left hand component are taking its place. From 5 to 8 there occur a series of deflections symmetrical to those between 4 and I . The resulting diagram, though so complex, is again nothing but the sum of the two simpler diagrams due to the separate components; (see Fig. 4e).
722
R. G. FRANKLIN, R.
E.
W. MADDISOS AND L. REEVE
Hence, to obtain the energy of the compound line, we must once again find the area of the compound diagram and divide by the mean dX for the components. The result will be 2 ( I .2x). We may now repeat the general result, already given in the first paper of this series, viz:-Whatever the nature of a line m a y be, whether simple or compound, and in the latter case whether doublet, triplet, etc., and whatever the width qf the slits employed, its relative energy i s obtnined by dividing the area qf the energy distribution diagram it gives by the mean valne af dX. It is obvious, however, that the use of slits of equal width results in simpler diagrams. Since these can be determined with greater accuracy and are convenient from other points of view, their employment is strongly recommended.
I
Cases where there i s n o need to work out Areas. In the case of some lines there is no need to 1 t 9. workout the areas of their diagrams in order to obtain their relative energy. This is the case for pure monochromatic lines whose energy is FIG.4c given directly by the heights of their triangles. The purity of lines can be determined from (a) photographs, or (b) from the value of the base of the graph diagram. If, in the case of equal slits, this does not exceed 2dX the line must be pure. Any excess aX is due to a corresponding wave length difference between the extreme components of a compound line. It follows from the above that the accurate determination of the true base of a diagram is as important as the measurement of the galvanometer deflections. In the case of the more intense lines this can be done fairly easily; but with the weaker lines it is more difficult, since the galvanometer deflections bounding the base are, necessarily, extremely - - small. In fact, in the case of very weak ___ _-lines, it may be found that the base ___ - -_ -_ _ _ - . _ _ determined is less than zdX, which we know is impossible. 5 6 7 8 FIG.4d Fortunately most of these lines in the case of the mercury spectrum are simple, so their relative energy content is best determined directly from the heights of their triangular diagrams. Even when they are known to be compound it is likely that smaller errors would be involved in doing likewise, than in calculating their areas (which involve base values, of course). Correction for Rejlection of Mirror. The relative energy distribution between the lines, calculated from their diagrams in the manner described, has to have one important correction ap-
,
m]
EXPERIMENTAL TE CHNIQCE O F PHOTOCHEMISTRY
723
plied to it before it can be used. This is due to the selective reflection of the metallic mirror which forms part of the optical system of the Hilger monochromator. It has been determined in this laboratory by one of us and a graphical representation of the results obtained is shown in Fig. j . From it the necessary corrections can he applied.
The Determination of Absolute Energy
We must now turn to the second of the energy characteristics, via; the total energy in the beam of light from the lamp used. Briefly, this is determined by comparing its energy with that from a Hefner lamp, the energy of which, under standard conditions, is known'. For this purpose a Moll surface thermopile ( I cm. in diameter) of internal resistance I O ohms. is employed in conjunction with a sensitive Gambrel1 moving coil galvanometer of internal resistance 23.6 ohms. and a sensitivity of about 6 mms. per microvolt. A. Disposition qf Apparatus for 1Measurement with Hefner Candle. The apparatus, the arrangement of which is shown in Fig. 6a, is mounted in a cupboard, free from draughts and blackened inside. A is a large slab of stone, blackened to a matt surface and placed behind the lamp. BC is the screen by means of which the radiation from the Hefner lamp D is cut off from or admitted to the thermoFIG.4e pile E. BC is also blackened, and arrangements are made for using it from the outside of the cupboard. The object of the stone slab A is to act as a background for the Hefner lamp which shall be in the same state of thermal equilibrium as the side C of the screen BC nearer the thermopile. The height of the flame of the Hefner lamp is adjusted by means of a cathetometer, observation being made through a circle in the blackened glass window of the front of the cupboard (a converted fume-cupboard). The thermopile is similarly adjusted so that its centre corresponds to the centre of the flame. The distance DE is I metre. G is the galvanometer, mounted outside the cupboard. Its sensitivity is determined by applying a P. D. of about I 5 microvolts at its terminals with the aid of a suitably arranged potentiometer. The Hefner lamp arranged as described above and burning under the usual standard conditions gives a mean deflection of 4.95 ems. corresponding to a P. D. of 7.89 microvolts. B. Dispositzon qf Apparatus for Measurement of Total Energy of Mercury L a m p Radiation. For determining the total energy, the lamp h (Fig. 6b) is mounted on an optical bench in the same way as described in connection with Fig. I and it is Gerlach: Physik. Z. 14, 577 (1913)
R. G . FRANKLIN, R. E. W. MADDISON AND L, REEVE
724
fitted with the usual diaphragm B. One condenser lens only (C) is employed, the water cell E is retained, and flush up against its back plate is placed the Moll thermopile D connected to the Gambrel1 galvanometer G. In order to obtain reasonable deflections when working with the intense beam from the mercury lamp, an additional series resista1;ce R of about 2 0 0 ohms is introduced. The light field passing the water cell is then examined. I n spite of the fact that the lens C is placed so as to give a parallel beam, the field obtained is only approximately uniform. It is therefore important for the determination of the total energy that the lamp should be in the very position in which it is to be used for the quantitative experiments and that the energy measured
240
300
360
420
480
540
600
FIG.5
by the thermopile should be taken with the receivers of the latter in exactly the position occupied normally by the front surface of the reaction cell. Further, owing to the fact that, the beam is not strictly uniform, it is necessary to explore the field to obtain a mean value for the total energy. The figure finally obtained for the latter is reduced to microvolts by determining the sensitivity of the galvanometer. Knowing the energy of the Hefner lamp in microvolts, it is now possible to express the energy of the beam of light from the mercury lamp under consideration in terms of Hefner candles; and, since a Hefner candle is equivalent to 9.42 X 102ergs per sq. cm. per second a t a distance of one metre, we can finally express the total energy in the beam of light from the lamp in absolute units. Finally, the energy distribution being known it is possible to state the quantity of radiant energy of any given wave length present in the beam falling upon the reaction vessel.
Losses by Reflection A certain amount of light is always lost by reflection at the surface of any medium, even if perfectly transparent to the incident radiation. This there-
EXPERIMENTAL TE CHXIQUE O F PHOTO CHiGMIYTRY
725
fore will occur a t the surface of the quartz plates and lenses normally used in photochemical work. The extent of the loss can be calculated from Ruben's figures for the refractive indices of quartz a t various wave lengths, in conjunction with Fresnels equation:-
where R = reflection a t wave length X, for normal incidence and for a single surface, and n = the refractive index for that wave length. For example:-
'"7 Fro. 62
for X 535 pp, n = 1.54663 and therefore R = 4.5%; for X 2 7 4 p p ! n = 1.58750 and therefore R = 5 . ~ 7 ~ . Since the effect of wave length upon this reflection is not very large, there is no need to take into account its effect a t the quartz surfaces inside the spectrometer when determining energy distributions. I t has to be allowed for only when dealing with absolute energy data.
FIG.6b
Correction for Infra Red Radiation passed by a 1 CM. Quartz Water Cell According to Coblentz, Long and Kahler', the intensities of the lines of the mercury infra-red spectrum for wave lengths shorter than I .4 p (with which we are particularly concerned) are approximately as follows :line a t 1.014 p : intensity about same as 0.436 p. LL LL LL line a t 1.128 p: " 0.406 p. 3 lines a t 1.2 p : intensity of each about 2 1 3 of 0.406 p . LL LL LL 2 lines a t 1.37 p : (' 2/3 L L 1 L P. Bur. Standards, Scientific Papers S o . jgo, p. 1.
726
R. G . FRANKLIX, R . E. W. MADDISON AND L . R E E V E
A Icm. quartz water cell, though absorbing entirely all infra-red radiation longer than I .4 p , will transmit, according to Aschkinassl:67.5% of 1.014 1.1. 73.5% of 1.128 ,u 31.570 of 1 . 2 p. 14'10
Of 1.37 p.
The total energy figures have therefore been corrected on this basis. It is recognised that the method is approximate, but it must suffice until new determinations of the infra-red spectrum of the mercury lamp can be carried out.
Summary ( I ) h complete account of the method of determining the energy distribution in the radiation from quartz mercury lamps, or any other light source, has been given. ( 2 ) The interpretation of the results obtained has been discussed, and the connection between the width of the slits used in the spectrometer, the nature of the line and the shape of the diagram it gives on the energy distribution diagram has been fully considered. ( 3 ) Finally, the method of determining the total energy in the beam of light employed has been discussed. We wish to thank Professor Allmand for the suggestion of writing this paper and for the interest he has taken in it, and also the Department of Scientific and Industrial Research for grants to us whilst Students in Training.
The Chemastry Department, Kings College, London. September, 1924. Aschkinass: Ann. Physik. 55, 415 (1895).
