Based on the wavelength of the light, the energy of the photons emitted by a sodium lamp is 17.74 X 10² kJ/mol.
The energy is given by the formula;
E = hv
where,
h is Planck's constant = 6.63 X 10⁻³⁴ Js
f is frequency of light
Also, f = c/λ
where,
c is velocity of light = 3.0 X 10⁸ m/s
λ is wavelength of light = 589 nm = 6.75 X 10⁻⁷ m
1 mole of sodium atom will emit 6.02 X 10²³ photons,
N = 6.02 X 10²³ photons,
Thus,
= E = Nhc/λ
= E = (6.02 X 10²³ X 6.63 X 10⁻³⁴ J.s X 3.0 X 10⁸ m/s)/6.75 X 10⁻⁷ m
= E = 119.74 X 10⁻³ / 6.75 X 10⁻⁷
= E = 17.74 X 10⁵ J/mol
= E = 17.74 X 10² kJ/mol
Therefore, the energy of the photons emitted by a sodium lamp is 17.74 X 10² kJ/mol.
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