Question

1.
Light near the middle of the ultraviolet region of the electromagnetic spectrum
has a frequency of 2.73 X 1016 s-1
a.
What is the wavelength of this radiation in meters (m)?
b.
What is the energy associated with this radiation in kcal?

Answer 1

Explanation:

Given that,

The frequency of electromagnetic spectrum is $2.73\times 10^{16}\ Hz$

(A) Let the wavelength of this radiation is $\lambda$. We know that,

$c=f\lambda\\\\\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{2.73\times 10^{16}}\\\\\lambda=1.09\times 10^{-8}\ m$

So, the wavelength of this radiation is $1.09\times 10^{-8}\ m$.

(B) Let E is the energy associated with this radiation. Energy of an electromagnetic radiation is given by :

$E=hf$

h is Planck's constant

$E=6.63\times 10^{-34}\times 2.73\times 10^{16}\\\\E=1.8\times 10^{-17}\ J$

1 kcal = 4184 J

It means,

$1.8\times 10^{-17}\ J=\dfrac{1}{4184}\times 1.8\times 10^{-17}\\\\=4.3\times 10^{-21}\ \text{kcal}$

Hence, this is the required solution.