Question

Problem 4: This problem deals with black bodies, photons and lasers. Martin runs out of light bulbs and decides to make one. He takes a 10 cm long wire with the circular cross-section of radius 1 mm. He hooks it up to electricity and manages to heat it up to 1300 K. • How many photons per second in a wavelength interval of 0.05 nm, cen- tered at 500 nm, does this wire emit? (6 points). • How strong laser would Martin have to use to obtain the same spectral emissivity as the wire produces (energy per unit time per unit surface per unit wavelength/frequency) at this wavelength interval? Assume the laser is tuned to only emit at this interval. Laser emits from the surface approximately equal to 1 mm? (6 points) • Since the wire emits like a blackbody, it will also emit at other visible wavelengths. How would you calculate the total emissivity of the wire in the visible part of the spectrum (400 nm to 700 nm? Sketch the derivation or argue in written form, you do not have to carry out the complete calculation. Can you use this to explain why tungsten bulbs shine as bright as "eco" ones but spend much more power? (6+2 points). A tungsten lamp is basically a wire heated to 2500 K.

Answer 1

- To find the number of photons in wavelength leange, we may Avendge the take given the x = x + x2 2 As a would be wavelength 0.05 nm & less than 500 greater than m the Encuen y leau Now; if we multiply the intensity distribution with surface Arla & use the given wavelength orange, we will get caring the hole, where it emit. i. The er, the Power Radiated is; P= IA = PCA For a given wowelength between s& dx А — ред Px dx - = pe 8The Adx d? 5 exp he - 1 CA dx - 8the² tada [explained at ) – 2)

le Page P dx = 64 x² n c ² d (12-21) (d, + 2z) " (expl 2h KT) -1 0 But the energy of ruitted photons should be equal to nhe & Px dx = ung n = Px dd , where hf is the ng energy of Single put the equo in this; Sowe forn, after putting the values given you Valuu purning You will find the no. of Photons enitted peu second