Question

What is the range of wavelength of the spectrum of white light in $\mathop A\limits^\circ$ ?
(A) $4000{A^0}$ to $5000 \mathop A\limits^\circ$
(B) $5000{A^0}$ to $6000 \mathop A\limits^\circ$
(C) $6000{A^0}$ to $8000 \mathop A\limits^\circ$
(D) All of the above

Answer 1

Hint : To solve this question, we need to look at the components of the colors that the white light consists of. Then with the help of the EM spectrum we can easily get the required range of the wavelength, which falls in the visible region.

Complete step by step answer
White light is that part of the electromagnetic radiation, which is visible to the human eyes. So the region of the EM spectrum, which consists of the white light, is termed as the visible region of the EM spectrum. When the white light is passed through a prism, then after getting refracted through the prism, it gets split into its seven components. This phenomenon is termed as dispersion. The seven components of the white lights thus obtained are represented by VIBGYOR. Here V stands for violet, I stands for indigo, B stands for blue, G stands for green, Y stands for yellow, O stands for orange, and R stands for red. These get split due to difference in their wavelengths. Their wavelength range from the blue colored light has the minimum wavelength of about $400nm$ , to the red colored light, which has the maximum wavelength of about $750nm$ . So the range of white light is from $400nm$ to $750nm$ . Now, we now that
$1nm = {10^{ - 9}}m$ …………………...(1)
$1 \mathop A\limits^\circ = {10^{ - 10}}m$ …………………...(2)
Dividing (1) by (2) we get
$\dfrac{{1nm}}{{1 \mathop A\limits^\circ }} = \dfrac{{{{10}^{ - 9}}m}}{{{{10}^{ - 10}}m}}$
$\Rightarrow 1nm = 10 \mathop A\limits^\circ$
Thus, the range of white can be written as from $4000 \mathop A\limits^\circ$ to $7500 \mathop A\limits^\circ$ .
So we see that all of the three ranges given in the option A, B, and C are correct.
Hence, the correct answer is option D.

Note
We should not get confused by the range given in the option C, which has a maximum wavelength of $8000 \mathop A\limits^\circ$ , different from the maximum wavelength of red light of $7500 \mathop A\limits^\circ$ . As both of the options A and B are correctly matching, so we have to consider all of the options to be correct, by assuming this difference to be negligible.