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Dual Nature of Radiation and Matter Ncert Solutions Physics Class 12th Physics Ncert Solutions Class 12th Physics Class 12th Dual Nature of Radiation and Matter

11.7 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?

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Payal Gupta | Contributor-Level 10

4 months ago

11.7 Power of the sodium lamp, P = 100 W

Wavelength of the emitted sodium light, $λ$ = 589 nm = 589 $\times 10^{- 9}$ m

Planck’s constant, h = 6.626 $\times 10^{- 34}$ Js

Speed of light, c = 3 $\times 10^{8}$ m/s

Energy per photon associated with the sodium light is given as:

$E$ = $\frac{h c}{λ}$ = $\frac{6.626 \times 10^{- 34} \times 3 \times 10^{8}}{589 \times 10^{- 9}}$ = 3.37 $\times 10^{- 19}$ J = $\frac{3.37 \times 10^{- 19}}{1.6 \times 10^{- 19}}$ eV = 2.11 eV

Let the number of photon delivered to the sphere = n

The equation of power can be written as $P = n E$

$n$ = $\frac{P}{E}$ = $\frac{100}{3.37 \times 10^{- 19}}$ photons/sec = 2.97 $\times 10^{20}$ photons/s

Therefore, every second, 2.97 $\times 10^{20}$ are delivered to the sphere.

Therefore, every second, 2.97 $\times 10^{20}$ are delivered to the sp

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11.7 Power of the sodium lamp, P = 100 W

Wavelength of the emitted sodium light, $λ$ = 589 nm = 589 $\times 10^{- 9}$ m

Planck’s constant, h = 6.626 $\times 10^{- 34}$ Js

Speed of light, c = 3 $\times 10^{8}$ m/s

Energy per photon associated with the sodium light is given as:

$E$ = $\frac{h c}{λ}$ = $\frac{6.626 \times 10^{- 34} \times 3 \times 10^{8}}{589 \times 10^{- 9}}$ = 3.37 $\times 10^{- 19}$ J = $\frac{3.37 \times 10^{- 19}}{1.6 \times 10^{- 19}}$ eV = 2.11 eV

Let the number of photon delivered to the sphere = n

The equation of power can be written as $P = n E$

$n$ = $\frac{P}{E}$ = $\frac{100}{3.37 \times 10^{- 19}}$ photons/sec = 2.97 $\times 10^{20}$ photons/s

Therefore, every second, 2.97 $\times 10^{20}$ are delivered to the sphere.

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