Question

When light of wavelength '$\lambda$' is incident on a photosensitive surface, photons of power 'P' are emitted. The number of photon 'n' emitted in time 't' is [h = Planck's constant, c = velocity of light in vacuum]

• A. $\frac{hc}{P\lambda t}$
• B. $\frac{P\lambda}{htc}$
• C. $\frac{P\lambda t}{hc}$
• D. $\frac{hP\lambda}{tc}$

Hint:

Total energy is power multiplied by time ($E = P \cdot t$). To get the number of packets, simply divide total energy by single packet energy: $\frac{Pt}{\left(\frac{hc}{\lambda}\right)} = \frac{P\lambda t}{hc}$. Dimensional analysis can also rule out wrong choices immediately!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks us to derive an expression for the total number of photons ($n$) emitted over a duration ($t$) given the source power ($P$) and wavelength ($\lambda$).

Step 2: Detailed Explanation:
The energy ($E$) of a single photon is given by Planck's relation: $$ E = \frac{hc}{\lambda} $$ If $n$ photons are emitted, the total energy radiated is $E_{\text{total}} = n \cdot E = \frac{nhc}{\lambda}$. Power ($P$) is defined as total energy divided by time ($t$): $$ P = \frac{E_{\text{total}}}{t} = \frac{nhc}{\lambda t} $$ Rearranging this algebraic formula to isolate the photon count variable $n$: $$ n = \frac{P\lambda t}{hc} $$

Step 3: Final Answer:
The total number of emitted photons is represented by $\frac{P\lambda t}{hc}$, matching option (C).