Maximum number of photons emitted by a bulb capable of producing monochromatic light of wavelength 550 nm is ………………….., if 100 V and 1A is supplied for one hour.

Options

A. `1 xx 10^(24)`
B. `5 xx 10^(24)`
C. `1 xx 10^(23)`
D. `5 xx 10^(23)`

Explanation

To find the maximum number of photons emitted by a bulb producing monochromatic light of wavelength 550 nm when supplied with 100 V and 1 A for one hour, we can follow these steps:

### Step 1: Calculate the energy of a single photon.
The energy (E) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) (Planck's constant) = \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( c \) (speed of light) = \( 3.00 \times 10^{8} \, \text{m/s} \)
- \( \lambda \) (wavelength) = \( 550 \, \text{nm} = 550 \times 10^{-9} \, \text{m} \)

Substituting the values, we get:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3.00 \times 10^{8} \, \text{m/s})}{550 \times 10^{-9} \, \text{m}} \]

### Step 2: Perform the calculation for energy of a photon.
Calculating this gives:
\[ E = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^{8})}{550 \times 10^{-9}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{550 \times 10^{-9}} \]
\[ E \approx 3.61 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the total energy supplied to the bulb.
The total energy (W) supplied to the bulb can be calculated using:
\[ W = V \times I \times t \]
where:
- \( V = 100 \, \text{V} \)
- \( I = 1 \, \text{A} \)
- \( t = 1 \, \text{hour} = 3600 \, \text{s} \)

Substituting the values:
\[ W = 100 \, \text{V} \times 1 \, \text{A} \times 3600 \, \text{s} \]
\[ W = 360000 \, \text{J} \]

### Step 4: Calculate the number of photons emitted.
The number of photons (N) emitted can be calculated using:
\[ N = \frac{W}{E} \]
Substituting the values:
\[ N = \frac{360000 \, \text{J}}{3.61 \times 10^{-19} \, \text{J}} \]

### Step 5: Perform the final calculation for the number of photons.
Calculating this gives:
\[ N \approx \frac{360000}{3.61 \times 10^{-19}} \]
\[ N \approx 1.00 \times 10^{24} \]

### Final Answer:
The maximum number of photons emitted by the bulb is approximately \( 1.00 \times 10^{24} \).

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