Question

The SI unit of time is the second, which is defined as 9,192,631,770 cycles of radiation associated with a certain emission process in the Cesium atom. Calculate the wavelength of this radiation (to 3 sig figs). In which region of the electromagnetic spectrum is the wavelength found?

Answer 1

Answer :  The wavelength of this radiation is, $3.26\times 10^{-2}m$ and in microwave region, the electromagnetic spectrum the wavelength is found.

Explanation : Given,

Frequency of radiation = $9192631770s^{-1}$

Formula used :

$\nu=\frac{c}{\lambda}$

where,

$\nu$ = frequency of radiation

$\lambda$ = wavelength of radiation

c = speed of light = $3\times 10^8m/s$

Now put all the given values in the above formula, we get:

$9192631770s^{-1}=\frac{3\times 10^8m/s}{\lambda}$

$\lambda=3.26\times 10^{-2}m$

Thus, the wavelength of this radiation is, $3.26\times 10^{-2}m$ and in microwave region, the electromagnetic spectrum the wavelength is found.

Answer 2

For waves:
speed = frequency x wavelength
speed = 3 x 10⁸ 
frequency = 9192631770 Hz
wavelength = 3 x 10⁸ / (9192631770)
wavelength = 0.033 meters
This wavelength lies in the region of microwaves.