Microwave radiation has a wavelength on the order of 1.0 cm. Calculate the frequency and the energy of a single photon of this radiation.
Calculate the energy of an Avogadro's number of photons (called an einstein) of this radiation

1.)Hz energy?
2.)J/photon?
3.) J/mol

Respuesta :

Answer :

(1) The frequency of photon is, [tex]3\times 10^{10}Hz[/tex]

(2) The energy of a single photon of this radiation is [tex]1.988\times 10^{-23}J/photon[/tex]

(3) The energy of an Avogadro's number of photons of this radiation is, 11.97 J/mol

Explanation : Given,

Wavelength of photon = [tex]1.0cm=0.01m[/tex]     (1 m = 100 cm)

(1) Now we have to calculate the frequency of photon.

Formula used :

[tex]\nu=\frac{c}{\lambda}[/tex]

where,

[tex]\nu[/tex] = frequency of photon

[tex]\lambda[/tex] = wavelength of photon

c = speed of light = [tex]3\times 10^8m/s[/tex]

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

[tex]\nu=\frac{3\times 10^8m/s}{0.01m}[/tex]

[tex]\nu=3\times 10^{10}s^{-1}=3\times 10^{10}Hz[/tex]    [tex](1Hz=1s^{-1})[/tex]

The frequency of photon is, [tex]3\times 10^{10}Hz[/tex]

(2) Now we have to calculate the energy of photon.

Formula used :

[tex]E=h\times \nu[/tex]

where,

[tex]\nu[/tex] = frequency of photon

h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]

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

[tex]E=(6.626\times 10^{-34}Js)\times (3\times 10^{10}s^{-1})[/tex]

[tex]E=1.988\times 10^{-23}J/photon[/tex]

The energy of a single photon of this radiation is [tex]1.988\times 10^{-23}J/photon[/tex]

(3) Now we have to calculate the energy in J/mol.

[tex]E=1.988\times 10^{-23}J/photon[/tex]

[tex]E=(1.988\times 10^{-23}J/photon)\times (6.022\times 10^{23}photon/mol)[/tex]

[tex]E=11.97J/mol[/tex]

The energy of an Avogadro's number of photons of this radiation is, 11.97 J/mol

Answer:

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Explanation:

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