A photon has a frequency of
Interpretation:
The frequency of a photon is to be converted into wavelength (in nm) and the statement, “does this frequency fall in the visible region?” is to be answered with the energy of photon in joules. Also, the energy for one mole of photons having this frequency is to be evaluated.
Concept introduction:
Electromagnetic wave has an electric field component and a magnetic field component having same wavelength and frequency.
The range of wavelengths (in nm) and the type of radiation are
The relationship between wavelength and frequency of an electromagnetic radiation is as follows:
Here,
A small discrete packet of energy that is associated with electromagnetic radiation is called a photon. One photon is equivalent to one quantum.
The energy of a photon can be expressed as follows:
Here, E is the energy of photon,
The relationship between meters
To convert meters
To convert
The relationship between mole and number of atoms or photons can be expressed as:
To convert number of photons to mole, conversion factor is
Answer to Problem 17QP
Solution:
(a)
(b)
(c)
Explanation of Solution
a) Convert frequency into wavelength, does it falls in visible region?
The frequency of a photon is
The wavelength (in nm) of photon can be evaluated as follows:
Substitute
Therefore, the wavelength of a photon is
As the microwave region has a range of
b) Energy (in joules) of photon.
The frequency of a photon is
The energy of photon is evaluated as shown below.
Substitute
Hence, the energy of a photon is
c) Energy (in joules) of 1 mole of photon all with this frequency.
The frequency of a photon is
The energy of a single photon
The energy for 1 mole of photons is evaluated as shown below.
Hence, the energy for one mole of photons is
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