At room temperature (300k), what is the significant contribution wavelength for the thermal radiation emitted by a body ?

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Correct — option (2), 9550 nm. Every body above absolute zero radiates, and the wavelength at which it radiates most strongly is fixed by its temperature through Wien's displacement law: the peak wavelength multiplied by the absolute temperature equals a constant of about 2.9 thousandths of a metre-kelvin. Put the room temperature of the stem into that relation — the paper writes it as 300k, meaning 300 kelvin — and the peak comes out at roughly 2.9 times ten to the minus three divided by 300, which is about 9.7 micrometres, or something under ten thousand nanometres. Of the four printed choices only 9550 nm lies anywhere near that figure; the exact value from the standard constant is a little above it, but the other three options are wrong by whole orders of magnitude rather than by a few per cent, so the intended answer is unmistakable. The physical meaning is worth holding on to. A body at everyday temperature emits its thermal radiation in the mid to far infrared, well beyond the red end of what the eye can see, which is why objects around us do not glow in the dark and why a camera that can see this radiation must be built with infrared detectors rather than ordinary optics. It is also the reason the atmospheric window between roughly eight and fourteen micrometres matters so much: that band is where the earth's surface, sitting near 300 kelvin, radiates most of its heat, and it is the band that greenhouse gases absorb. Only when a body is heated to a thousand kelvin or more does its peak move far enough toward the visible for it to appear red hot, and only at several thousand kelvin does it look white.

Why the other options are wrong — (a) 500 nm sits in the middle of the visible spectrum, in the green, and it is the peak emission wavelength not of a room but of the surface of the Sun, which is at roughly 5,800 kelvin. Wien's law makes the mismatch stark: to peak at 500 nm a body would have to be some twenty times hotter than the room described in the stem. This choice tests whether a candidate has confused the wavelength at which the eye is most sensitive, and the wavelength at which sunlight peaks, with the radiation emitted by an ordinary object at ordinary temperature.  (c) 1500 nm is in the near infrared, just beyond the visible, and by Wien's law it corresponds to a body at roughly 1,900 kelvin — comparable to the filament of an incandescent lamp rather than to a room. It is a familiar number for another reason entirely, being one of the standard transmission bands of optical fibre communication, and that familiarity is what makes it a plausible-looking choice. It is nonetheless more than six times shorter than the wavelength at which a 300 kelvin body radiates most strongly.  (d) 3000 nm, or three micrometres, is in the mid infrared and corresponds by Wien's law to a temperature of around 970 kelvin — a body hot enough to glow a dull red. It is the closest of the three wrong choices and the one a candidate might reach for after correctly deciding that the answer must be infrared, having remembered the direction of the relation without carrying the arithmetic through. The calculation is worth doing rather than estimating: dividing the Wien constant by 300 gives close to ten micrometres, not three.

Concept: A body in thermal equilibrium emits a continuous spectrum of electromagnetic radiation whose shape depends only on its temperature, and two laws summarise that spectrum. Wien's displacement law fixes where the peak lies: the product of the peak wavelength and the absolute temperature is a constant, about 2.9 times ten to the minus three metre-kelvin, so the hotter the body the shorter the wavelength at which it radiates most strongly. The Stefan-Boltzmann law fixes how much it radiates in total: the power emitted per unit area rises as the fourth power of the absolute temperature, so a modest rise in temperature produces a large rise in emission. Together they explain the everyday sequence of a heated object — dark but radiating in the infrared at room temperature, dull red near a thousand kelvin, orange and then yellow as it climbs, white at several thousand. They also explain the planetary energy balance: the Sun at about 5,800 kelvin radiates mainly in the visible and near infrared, which passes readily through the atmosphere; the earth's surface at about 300 kelvin re-radiates in the far infrared around ten micrometres, which greenhouse gases absorb, and that asymmetry is the mechanism of the greenhouse effect.

State PCS 2024 Q53 — Science & Technology PYQ with Answer

State PCS 2024 Q53 — Science & Technology PYQ with Answer