A 100W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm. (a) What is the energy per photon associated with the sodium light? (b) At what rate are the photons delivered to the sphere?
Given: The power of sodium lamp is 100 W and the wavelength of the sodium light is 589 nm .
a)
The energy of photon is given as,
E = h c λ
Where, Planck’s constant is h , the speed of light is c and the wavelength is λ .
By substituting the given values in the above equation, we get
E = 6.626 × 10 − 34 × 3 × 10 8 589 × 10 − 9 = 3.37 × 10 − 19 J = 2.11 eV
Thus, the energy per photon associated with sodium light is 2.11 eV .
b)
The number of photons delivered per second is given as,
n = P E
Where, the power is P and the energy is E .
By substituting the given values in the above equation, we get
n = 100 3.37 × 10 − 19 ≈ 3 × 10 20 photons / s
Thus, the number of photons delivered to the sphere per second is 3 × 10 20 .
Given: The power of sodium lamp is
a)
The energy of photon is given as,
Where, Planck’s constant is
By substituting the given values in the above equation, we get
Thus, the energy per photon associated with sodium light is
b)
The number of photons delivered per second is given as,
Where, the power is
By substituting the given values in the above equation, we get
Thus, the number of photons delivered to the sphere per second is
