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

Step-by-step explanation:

Given that,

The frequency of electromagnetic spectrum is
`2.73* 10^(16)\ Hz`

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

`c=f\lambda\\\\\lambda=(c)/(f)\\\\\lambda=(3* 10^8)/(2.73* 10^(16))\\\\\lambda=1.09* 10^(-8)\ m`

So, the wavelength of this radiation is
`1.09* 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* 10^(-34)* 2.73* 10^(16)\\\\E=1.8* 10^(-17)\ J`

1 kcal = 4184 J

It means,

`1.8* 10^(-17)\ J=(1)/(4184)* 1.8* 10^(-17)\\\\=4.3* 10^(-21)\ \text{kcal}`

Hence, this is the required solution.