Question

Use a computer to calculate Planck's radiation law for a temperature of 3000 K, which is the temperature of a typical tungsten filament in an incandescent light bulb. Plot the intensity versus wavelength. (a) How much of the power is in the visible region (400-700nm) compared with the ultraviolet and infrared? (b) What is the ratio of the intensity at 400 nm and 700 nm to the wavelength with maximum intensity?

Answer 1

Ans To solve nis Paoblem, we the planck's Yadiotion law. Use Plank's 3adiation law 9ives POwey Tadia kd per unit the aYea Per unit woveleng th fom o Con be expyessed black body and it mothema tically as follow e ca, T) anch hcakT here plank's ha 6.6a6 x to constont Speed o light, c= 3x168 mls Diagram;- uniuw The follooing dragram shows femperoture cveleng th Vexsus o spectrm of light Rayleight - jeans law 5000k Plank'sLowr wave lengih of 000 000 3000 Temperatore vistble

Giiven that he temperature of the -tungsn filamen t T = 3,000 k Foom the Dfagram he manimum wavelengh emнted fomm Gilamen A -966 лm maя Рower in the visible seglon Сon be obilarned by inRgrating the - 400 пm to As 0o nm о элhса eсяд da (ра) я5 ha e сэ) Re-aTange the Ая thelak о6 н09.го J алhса еСaт)-Са РС-р) fe calcuiations of constan ts - ) с3оховnlo)?) 8тhса J.S 8т 6.686x(0 j.5 3.746х 1616 -3и s9) (30 х 1 m1s) С6.686 x16 hc еxp aкт -93 3K) C3000k) (138 Y16

y.8x10 m еxp Substitute al he constant vo lues in the ea одома - (u.8 х105m) - (6 e(4т)> (3746X10 5 Let us Сonsides a - a and К- 4.в X165 then dys d1 hen A ч00, Хa- 00 11 above men integyal fart of the Aа С4.8 х168m)[a da л-5 хр. "

Using scientihic numenico iodegration method -) Gon TO0 -300 e k 39980000e k-11600e 8195000000 k -k k88160000e - 13171800000000t6ye K (104)- K1317100oo00e (hook) ki 1344000e Nou Substituting Ke 4.8x10°m and simpliky K/7 Powes in the visble begron can be Obtalnad by using eq 3.m2.s (A,T)3746(o' 3-71 xlo wim2- area emitted fo ol visible are Per unt hese PoweyS cwavelengths Power emitted for Overali aaveleng Hhs can be calculated as follows (3000 k )t (567 lo wm 4.99 x i06 Wma

Frachon oj light in the visible "segion &n be calculatked follea's as e Сат) 3-71x105 m R o.08 Rahio of intensities at A, a wih 0 Can be calcolaled as follows aThe (uo0)5r(6.636xio.5)(3xt0°mls) fuoonm )C38 xio^kas(3000 L966 (2,T) ahc (966)5(6-636x105-5)(3Mnls a3 66mm)(1-38 * Il0 ma C3000k) o.073 8xhc2 7o0)5C.636xt63"^s)(3xi03 m/s)J (10onm)(1-38 *lo33m*kg\s1) (3000k)-T 00 CT) t06 (a,T) (n66)6636 7(3Yi0mis)(966 nm) (1-36 6 C3o00) o.754