Answer:
1.98x10⁻¹² kg
Explanation:
The energy of a photon is given by:
h is Planck's constant, 6.626x10⁻³⁴ J·s
c is the speed of light, 3x10⁸ m/s
and λ is the wavelenght, 671 nm (or 6.71x10⁻⁷m)
Now we multiply that value by Avogadro's number, to calculate the energy of 1 mol of such protons:
Finally we calculate the mass equivalence using the equation:
The mass equivalence of 1 mole of photons of this wavelength is equal to [tex]1.78 \times 10^{-11} \;kg[/tex]
Given the following data:
We know that the speed of light is [tex]3 \times 10^8[/tex] m/s.
Planck constant = [tex]6.626 \times 10^{-34}\;J.s[/tex]
Avogadro constant = [tex]6.02 \times 10^{23}[/tex]
To determine the mass equivalence of 1 mole of photons of this wavelength:
First of all, we would calculate the energy associated with the photons of this wavelength by using the Planck-Einstein relation:
Mathematically, Planck-Einstein relation for photon energy is given by the formula:
[tex]E = hf = h\frac{v}{\lambda}[/tex]
Where:
Substituting the parameters into the formula, we have;
[tex]E = \frac{6.626 \times 10^{-34} \; \times \;3 \times 10^8 }{6.71 \times 10^{-7}} \\\\E = \frac{1.99 \times 10^{-25}}{6.71 \times 10^{-7}} \\\\E=2.96 \times 10^{-19} \;Joules[/tex]
For the energy of 1 mole of photons:
[tex]E = 2.96 \times 10^{-19} \times 6.02 \times 10^{23}\\\\E = 1.78 \times 10^5 \; Joules[/tex]
Now, we can find the mass equivalence of 1 mole of photons by using the formula:
[tex]E = mc^2\\\\m = \frac{E}{c^2} \\\\m = \frac{1.78 \times 10^5}{(3.0 \times 10^8)^2} \\\\m = \frac{1.78 \times 10^5}{(9.0 \times 10^{16})}\\\\m = 1.78 \times 10^{-11} \;kg[/tex]
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