Question

Iron begins to glow at 1,100° C, what would be its wavelength of maximum intensity?

Answer 1

`lamda_"max" = "2100 nm"`

Explanation:

The idea here is that you're looking for the wavelength of the black-body radiation emitted by the iron at that temperature.

As you know, black-body radiation refers to the electromagnetic radiation emitted by a black object while held at constant temperature.

The important thing to remember here is that the intensity of this radiation depends exclusively on the absolute temperature, i.e. the temperature expressed in Kelvin, of the object.

The relationship between the maximum intensity of the black-body radiation emitted by an object and the wavelength at which it takes place is given by the Wien displacement law equation

`color(blue)(lamda_"max" = b/T)" "`, where

`lamda_"max"` - the wavelength at which the intensity of the radiation is maximum
`b` - Wien's displacement constant, equal to `2.89777 * 10^(-3)"m K"`
`T` - the temperature of the object, always expressed in Kelvin!

In your case, you know that the temperature of the iron is set at `1100""^@"C"`. This is equivalent to

`T = 1100 + 273.15 = "1373.15 K"`

This means that the wavelength at which the intensity of its emitted radiation is maximum will be

`lamda_"max" = (2.89777 * 10^(-3) color(red)(cancel(color(black)("K"))))/(1373.15 color(red)(cancel(color(black)("K")))) = 2.11 * 10^(-6)"m"`

Expressed in nanometers and rounded to two sig figs, the answer will be

`lamda_"max" = color(green)("2100 nm")`

This wavelength places the radiation in the infrared region of the electromagnetic spectrum.