Question

Microwave radiation has a wavelength on the order of 1.7 cm. Calculate the frequency (in Hz) and the energy (in J) of a single photon of this radiation.

Answer 1

Answer:

$\nu = 1.76x10^{10}Hz$, $E = 1.16x10^{-23}J$

Explanation:

The frequency can be found by means of the next expression:

$c = \lambda \nu$ (1)

Where c is the speed of light, $\lambda$ is the wavelength and $\nu$ is the frequency.

$\nu$ can be isolated from equation 1:

$\nu = \frac{c}{\lambda}$ (2)

Notice that is necessary to express the wavelength in meters:

$1.7cm . \frac{1m}{100cm}$ --- $0.017m$

$\lambda = 0.017m$

Replacing those values in equation (2) it is gotten:

$\nu = \frac{3.00x10^{8}m/s}{0.017m}$

$\nu = 1.76x10^{10}s^{-1}$

But $1Hz = 1s^{-1}$

$\nu = 1.76x10^{10}Hz$

So, the frequency of the photon is $\nu = 1.76x10^{10}Hz$.

The energy of a photon is defined as:

$E = \frac{hc}{\lambda}$ (3)

Where h is the planck's constant, c is the speed of light and $\lambda$ is the wavelength.

$E = \frac{(6.62x10^{-34}J.s)(3.00x10^{8}m/s)}{(0.017m)}$

$E = 1.16x10^{-23}J$

Hence, the energy of the photon is $E = 1.16x10^{-23}J$.

Answer 2

The frequency of the wavelength of microwave radiation is 1.76×10¹⁰ Hz and the energy of a single photon of this radiation is 1.16×10⁻²³ J.

What is frequency?

Frequency of wave is the number of waves, which is passed thorough a particular point at a unit time. It can be given as,

$f=\dfrac{c}{\lambda}$

Here,(c) is the speed of the wave and (λ) is the wavelength of the wave.

Microwave radiation has a wavelength on the order of 1.7 cm or 0.017 m.  As the speed of the light is 3×10⁸ m/s approximately. Hence, the frequency of it,

$f=\dfrac{3\times10^8}{0.017}\\f=1.76\times10^{10}\rm\; Hz$

Now the energy of the photon is given as,

$E=hf$

Here, h is the planks constant. Hence,

$E=6.62\times10^{-34}(1.76\times10^{10})\\E=1.16\times10^{-23}\rm J$

Hence, the frequency of the wavelength of microwave radiation is 1.76×10¹⁰ Hz and the energy of a single photon of this radiation is 1.16×10⁻²³ J.

Learn more about the frequency here;

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