Respuesta :
The Planck equation and rules of direct proportions can be found that the amount of energy emitted by sodium the answer is;
E = 2.2 10⁻¹³ J
Planck's equation establishes a relationship for the energy of photons
E = h f
c = λ f
E = [tex]\frac{h \ c}{\lambda}[/tex]
Where E is the energy, h the Planck constant (h = 6.63 10⁻³⁴ J s), f the frequency of radiation, c the speed of light and λ the wavelength
The energy emitted by each sodium atom is the energy of the emitted radiation that has a wavelength of 590 nm, two lines close together, indicate that each atom emits a photon, its energy is
E₀ = [tex]\frac{6.63 \ 10^{-34} \ 3 \ 10^8}{ 590 \ 10^{-9}}[/tex]
E₀ = 3.37 10⁻¹⁹ j
We look for the mass of a mole of sodium in the periodic table
PM = 29.9897uma ( [tex]\frac{1.66 \ 10^{-17} kg}{1 una}[/tex]) = 49.78 10⁻²⁷ kg
With a direct rule of proportions we can find the atoms of sodium in the lamp. If in mol of sodium it has a mass 49.78 10⁻²⁷ kg and has avogadro number 6.022 10²³ atoms. How many atoms are there in 45.8 10⁻⁹ kg
# sodium atoms = [tex]\frac{49.78\ 10^{-27} \ 6.022 \ 10^{23}}{ 45.8 \ 10^{-9}}[/tex]
#_atom Sodium = 6.54 10⁵ Sodium atoms.
Let's use a direct ratio rule, If a sodium atom emits an energy Eo, how much energy do you emit? 6.54 105 atoms
E = Eo # _atmos / 1 atom
E = 3.37 10⁻¹⁹ 6.54 10⁵
E = 2.2 10⁻¹³ J
In conclusion, using the Planck equation and direct proportions rules we can find the amount of energy emitted by sodium, the answer is;
E = 2.2 10⁻¹³ J
Learn more about the Planck equation here:
https://brainly.com/question/18013128
