sodium vapor lamps, used for public lighting, emit 489nm yellow light. what energy is emitted by:
(a) an excited sodium atom when it generates a photon?
(b) 1 mol of excited sodium atoms at this wavelength?
E= hc/wavelength.
h is Planck's constant.
C is light velocity = 3E8 m/s
wavelength is 489 nm convert to m.
I wonder if you meant 589 and not 489?
To determine the energy emitted by an excited sodium atom when it generates a photon, we can use the equation:
E = hc / λ
Where:
E is the energy of the photon,
h is the Planck's constant (6.626 x 10^-34 J⋅s),
c is the speed of light in a vacuum (3.0 x 10^8 m/s),
and λ is the wavelength of the light emitted.
(a) Energy emitted by an excited sodium atom:
By substituting the given wavelength (λ = 489 nm = 489 x 10^-9 m) into the equation, we can find the energy emitted by a single sodium atom:
E = (6.626 x 10^-34 J⋅s) × (3.0 x 10^8 m/s) / (489 x 10^-9 m)
Simplifying the equation yields:
E = 4.046 x 10^-19 J
Therefore, an excited sodium atom emits photons with an energy of approximately 4.046 x 10^-19 joules.
(b) Energy emitted by 1 mol of excited sodium atoms:
To calculate the energy emitted by 1 mole of excited sodium atoms, we need to determine the number of excited sodium atoms in 1 mol.
Avogadro's number states that there are approximately 6.022 x 10^23 atoms in 1 mole of a substance. Since we are considering excited sodium atoms, this value remains the same.
Therefore, the energy emitted by 1 mole of excited sodium atoms would be:
Energy = (4.046 x 10^-19 J) × (6.022 x 10^23 atoms)
By multiplying these values together, we find:
Energy ≈ 2.437 x 10^5 J
Therefore, 1 mol of excited sodium atoms emits energy of approximately 2.437 x 10^5 joules.