Respuesta :
Answer:
For A: The energy of the given amount of photons for infrared radiation is [tex]1.271\times 10^5J[/tex]
For B: The energy of the given amount of photons for infrared radiation is [tex]4.026\times 10^5J[/tex]
For C: The energy of the given amount of photons for infrared radiation is [tex]1.355\times 10^6J[/tex]
Explanation:
The relationship between energy and frequency is given by Planck's equation, which is:
[tex]E=n\rimes N_A\times \frac{hc}{\lambda}[/tex] ......(1)
where,
h = Planck's constant = [tex]6.62\times 10^{-34}Js[/tex]
E = energy of the light
c = speed of light = [tex]3\times 10^8m/s[/tex]
[tex]\lambda[/tex] = wavelength of light
[tex]N_A[/tex] = Avogadro's number = [tex]6.022\times 10^{23}[/tex]
n = number of moles of photons = 1.70 moles
Conversion factor used: [tex]1m=10^9nm[/tex]
- For A:
Wavelength of infrared radiation = [tex]1600nm=1.6\times 10^6m[/tex]
Putting values in equation 1, we get:
[tex]E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{1.6\times 10^{-6}}\\\\E=1.271\times 10^5J[/tex]
Hence, the energy of the given amount of photons for infrared radiation is [tex]1.271\times 10^5J[/tex]
- For B:
Wavelength of visible light = [tex]505nm=5.05\times 10^7m[/tex]
Putting values in equation 1, we get:
[tex]E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{5.05\times 10^{-7}}\\\\E=4.026\times 10^5J[/tex]
Hence, the energy of the given amount of photons for infrared radiation is [tex]4.026\times 10^5J[/tex]
- For C:
Wavelength of ultraviolet radiation = [tex]150nm=1.5\times 10^7m[/tex]
Putting values in equation 1, we get:
[tex]E=1.7\times 6.022\times 10^{23}\times \frac{6.62\times 10^{-34}\times 3\times 10^8}{1.5\times 10^{-7}}\\\\E=1.355\times 10^6J[/tex]
Hence, the energy of the given amount of photons for infrared radiation is [tex]1.355\times 10^6J[/tex]
The energy stored in infrared radiation is 12.4 * 10⁻²⁰ J
The frequency (f) of a photon is given by:
f = c/λ
where c is the speed of light = 3 * 10⁸ m/s and λ is the wavelength.
a) λ = 1600 nm = 1600 * 10⁻⁹ m Hence:
f = c/λ = 3 * 10⁸ / 1600 * 10⁻⁹ = 1.875 * 10¹⁴ Hz
The energy (E) stored in a photon is:
E = hf;
h is Planck constant = 6.626 * 10⁻³⁴ Js
E = 6.626 * 10⁻³⁴ Js * 1.875 * 10¹⁴ Hz = 12.4 * 10⁻²⁰ J
b) λ = 505 nm = 505 * 10⁻⁹ m Hence:
f = c/λ = 3 * 10⁸ / 505 * 10⁻⁹ = 5.9 * 10¹⁴ Hz
The energy (E) stored in a photon is:
E = hf;
h is Planck constant = 6.626 * 10⁻³⁴ Js
E = 6.626 * 10⁻³⁴ Js * 5.9 * 10¹⁴ Hz = 3.9 * 10⁻¹⁶ J
c) λ = 150 nm = 150 * 10⁻⁹ m Hence:
f = c/λ = 3 * 10⁸ / 150 * 10⁻⁹ = 2 * 10¹⁵ Hz
The energy (E) stored in a photon is:
E = hf;
h is Planck constant = 6.626 * 10⁻³⁴ Js
E = 6.626 * 10⁻³⁴ Js * 2 * 10¹⁵ Hz = 132.5 * 10⁻²⁰ J
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