Sodium vapor lamps, used for public lighting, emit yellow light of wavelength 589 nm. How much energy is emitted by 5.00 mg of sodium atom emitting light at this wavelength?
To determine the energy emitted by 5.00 mg of sodium atoms emitting light at a wavelength of 589 nm, we can use the equation:
E = hc/λ
Where:
E is the energy,
h is Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light (3.00 x 10^8 m/s),
and λ is the wavelength of light.
First, let's convert the mass of sodium from milligrams (mg) to kilograms (kg):
5.00 mg = 5.00 x 10^-6 kg
Now, we can substitute the values into the equation:
E = (6.626 x 10^-34 J·s) × (3.00 x 10^8 m/s) / (589 x 10^-9 m)
Calculating the expression inside the brackets first:
(6.626 x 10^-34 J·s) × (3.00 x 10^8 m/s) = 1.9878 x 10^-25 J·m
Now divide this by the wavelength:
1.9878 x 10^-25 J·m / (589 x 10^-9 m)
Simplifying the equation:
(1.9878 x 10^-25 J·m) / (589 x 10^-9 m) = 3.37355 x 10^-17 J
Therefore, 5.00 mg of sodium atoms emitting light at a wavelength of 589 nm will emit approximately 3.37355 x 10^-17 Joules of energy.