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A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb.
- a)3 x 1020 s-1
- b)2 x 10-20 s-1
- c)2 x 1020 s-1
- d)1 x 10-20 s-1
Correct answer is option 'C'. Can you explain this answer?
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A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calcul...
Power of the bulb = 100 watt = 100 J s-1 Energy of one photon E = hv = hc/λ
Number of photons emitted
Number of photons emitted
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A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calcul...
To calculate the number of photons emitted per second by the bulb, we can use the formula:
Number of photons = Power / Energy of each photon
1. Calculate the energy of each photon:
The energy of a photon can be calculated using the formula:
Energy of photon = Planck's constant (h) * speed of light (c) / wavelength
Given:
- Wavelength (λ) = 400 nm = 400 x 10^-9 m
- Planck's constant (h) = 6.626 x 10^-34 J·s
- Speed of light (c) = 3 x 10^8 m/s
Substituting these values into the formula, we have:
Energy of photon = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (400 x 10^-9 m)
= 4.9695 x 10^-19 J
2. Calculate the power of the bulb:
Given:
- Power (P) = 100 W
3. Calculate the number of photons emitted per second:
Using the formula mentioned earlier, we can now calculate the number of photons emitted per second:
Number of photons = Power / Energy of each photon
= (100 W) / (4.9695 x 10^-19 J)
= 2.01 x 10^20 s^-1
Therefore, the correct answer is option C: 2 x 10^20 s^-1.
Number of photons = Power / Energy of each photon
1. Calculate the energy of each photon:
The energy of a photon can be calculated using the formula:
Energy of photon = Planck's constant (h) * speed of light (c) / wavelength
Given:
- Wavelength (λ) = 400 nm = 400 x 10^-9 m
- Planck's constant (h) = 6.626 x 10^-34 J·s
- Speed of light (c) = 3 x 10^8 m/s
Substituting these values into the formula, we have:
Energy of photon = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (400 x 10^-9 m)
= 4.9695 x 10^-19 J
2. Calculate the power of the bulb:
Given:
- Power (P) = 100 W
3. Calculate the number of photons emitted per second:
Using the formula mentioned earlier, we can now calculate the number of photons emitted per second:
Number of photons = Power / Energy of each photon
= (100 W) / (4.9695 x 10^-19 J)
= 2.01 x 10^20 s^-1
Therefore, the correct answer is option C: 2 x 10^20 s^-1.
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A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb.a)3 x 1020s-1b)2 x 10-20 s-1c)2 x 1020s-1d)1 x 10-20s-1Correct answer is option 'C'. Can you explain this answer?
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