A sodium bulb of 150W radiates 8 percent of the absorbed energy as yel...
Given data:
- Power of sodium bulb (P) = 150W
- Percentage of absorbed energy radiated as yellow light (R) = 8%
- Wavelength of yellow light (λ) = 4000 angstroms
Calculating the absorbed energy:
The power of the bulb represents the rate at which it consumes energy. Therefore, the energy absorbed by the bulb per second can be calculated using the formula:
Energy absorbed (E) = Power (P) x Time (t)
Since the time is not given, we will assume it to be 1 second for simplicity.
Hence, E = P x t = 150W x 1s = 150 Joules
Calculating the energy radiated as yellow light:
The percentage of absorbed energy that is radiated as yellow light is given as 8%. Therefore, the energy radiated as yellow light can be calculated using the formula:
Energy radiated as yellow light (E_yellow) = R/100 x E
Substituting the given values, we get:
E_yellow = 8/100 x 150 Joules = 12 Joules
Calculating the number of quanta emitted:
To calculate the number of quanta emitted, we need to convert the energy radiated as yellow light (E_yellow) into quanta using the formula:
Energy (E) = Number of quanta (n) x Energy per quantum (E_q)
The energy per quantum can be calculated using the equation:
E_q = hc/λ
Where:
h = Planck's constant (6.626 x 10^-34 J.s)
c = speed of light (3 x 10^8 m/s)
λ = wavelength of yellow light (4000 angstroms)
Converting the wavelength from angstroms to meters:
1 angstrom = 10^-10 meters
4000 angstroms = 4000 x 10^-10 meters = 4 x 10^-7 meters
Substituting the values into the equation, we get:
E_q = (6.626 x 10^-34 J.s x 3 x 10^8 m/s) / (4 x 10^-7 m)
E_q = 4.9695 x 10^-19 Joules
Now, we can calculate the number of quanta emitted:
n = E_yellow / E_q
n = 12 Joules / (4.9695 x 10^-19 Joules)
n ≈ 2.41 x 10^19 quanta
Therefore, the sodium bulb emits approximately 2.41 x 10^19 quanta of yellow light per second.
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