Let `(n_r) and (n_b) be respectively the number of photons emitted by a red bulb and a blue blub of equal power in a given time.

Options

A. `n_(r) = n_(b)`
B. `n_(l) lt b_(b)`
C. `n_(R) gt n_(b)`
D. nothing can be predicted

Explanation

To solve the problem of comparing the number of photons emitted by a red bulb and a blue bulb of equal power, we can follow these steps:

### Step 1: Understand the relationship between energy, power, and photons
The energy of a single photon can be expressed using Planck's law:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant,
- \(c\) is the speed of light,
- \(\lambda\) is the wavelength of the light.

### Step 2: Relate power to energy and time
The power \(P\) of the bulb is defined as the energy emitted per unit time:
\[ P = \frac{E_{total}}{t} \]
If we consider the total energy emitted in time \(t\), it can be expressed as:
\[ E_{total} = Pt \]

### Step 3: Calculate the number of photons emitted
Let \(n\) be the number of photons emitted. The total energy can also be expressed as the product of the number of photons and the energy per photon:
\[ E_{total} = n \cdot E \]
Substituting for \(E\) from Planck's law:
\[ E_{total} = n \cdot \frac{hc}{\lambda} \]
Equating the two expressions for \(E_{total}\):
\[ Pt = n \cdot \frac{hc}{\lambda} \]
From this, we can solve for \(n\):
\[ n = \frac{Pt \lambda}{hc} \]

### Step 4: Apply this to both the red and blue bulbs
Let \(n_r\) be the number of photons emitted by the red bulb and \(n_b\) be the number of photons emitted by the blue bulb. We can express them as:
\[ n_r = \frac{Pt \lambda_r}{hc} \]
\[ n_b = \frac{Pt \lambda_b}{hc} \]

### Step 5: Compare \(n_r\) and \(n_b\)
To find the ratio of the number of photons emitted by the red and blue bulbs:
\[ \frac{n_r}{n_b} = \frac{\lambda_r}{\lambda_b} \]
Since the wavelength of red light (\(\lambda_r\)) is greater than the wavelength of blue light (\(\lambda_b\)), we have:
\[ \lambda_r > \lambda_b \]
Thus:
\[ \frac{n_r}{n_b} > 1 \quad \Rightarrow \quad n_r > n_b \]

### Conclusion
The number of photons emitted by the red bulb is greater than that emitted by the blue bulb.