Question

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

Answer 1

Do you do professor Huang's Chemistry Class?

Step-by-step explanation:

Sorry if I may have offended you.

Answer 2

(1) The frequency of photon is,
`3* 10^(10)Hz`

(2) The energy of a single photon of this radiation is
`1.988* 10^(-23)J/photon`

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

Explanation : Given,

Wavelength of photon =
`1.0cm=0.01m` (1 m = 100 cm)

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

Formula used :

`\\u=(c)/(\lambda)`

where,

`\\u` = frequency of photon

`\lambda` = wavelength of photon

c = speed of light =
`3* 10^8m/s`

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

`\\u=(3* 10^8m/s)/(0.01m)`

`\\u=3* 10^(10)s^(-1)=3* 10^(10)Hz`
`(1Hz=1s^(-1))`

The frequency of photon is,
`3* 10^(10)Hz`

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

Formula used :

`E=h* \\u`

where,

`\\u` = frequency of photon

h = Planck's constant =
`6.626* 10^(-34)Js`

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

`E=(6.626* 10^(-34)Js)* (3* 10^(10)s^(-1))`

`E=1.988* 10^(-23)J/photon`

The energy of a single photon of this radiation is
`1.988* 10^(-23)J/photon`

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

`E=1.988* 10^(-23)J/photon`

`E=(1.988* 10^(-23)J/photon)* (6.022* 10^(23)photon/mol)`

`E=11.97J/mol`

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