Values of work function (\(W_0\)) for a few metals are given below. The number of metals which will show photoelectric effect when light of wavelength 400 nm falls on it is _________.
| Metal | Li | Na | K | Mg | Cu | Ag |
|---|---|---|---|---|---|---|
| \(W_0 \text{ (eV)}\) | 2.42 | 2.3 | 2.25 | 3.7 | 4.8 | 4.3 |
Given constants:
- \( h = 6.6 \times 10^{-34} \text{ J s} \)
- \( c = 3 \times 10^8 \text{ m s}^{-1} \)
- \( e = 1.6 \times 10^{-19} \text{ C} \)
Detailed Step-by-Step Solution
The photoelectric effect only occurs when the energy of the incident photon (\(E\)) is greater than or equal to the work function (\(W_0\)) of the metal.
Step 1: Formula for Photon Energy in eV
The energy of a photon is \( E = \frac{hc}{\lambda} \) in Joules. To convert Joules to electron-volts (eV), we divide by the charge of an electron (\(e\)).
Step 2: Substitute the Given Values
- \( \lambda = 400 \text{ nm} = 400 \times 10^{-9} \text{ m} \)
- \( h = 6.6 \times 10^{-34} \text{ J s} \)
- \( c = 3 \times 10^8 \text{ m/s} \)
- \( e = 1.6 \times 10^{-19} \text{ C} \)
Let's simplify the numerator and denominator:
\( \text{Denominator} = 640 \times 10^{-28} = 6.4 \times 10^{-26} \)
Now, divide them:
\( E \approx 3.09 \text{ eV} \)
Step 3: Compare with Work Functions (\(W_0\))
For the photoelectric effect to take place, the condition is \( E > W_0 \). We check which metals have a work function less than 3.09 eV.
- ✅ Li: \( 2.42 < 3.09 \) (Effect observed)
- ✅ Na: \( 2.3 < 3.09 \) (Effect observed)
- ✅ K: \( 2.25 < 3.09 \) (Effect observed)
- ❌ Mg: \( 3.7 > 3.09 \) (No emission)
- ❌ Cu: \( 4.8 > 3.09 \) (No emission)
- ❌ Ag: \( 4.3 > 3.09 \) (No emission)
Conclusion: Only 3 metals (Li, Na, and K) will show the photoelectric effect. Therefore, the answer is 3.
Mastering the Photoelectric Effect
The Photoelectric Effect is a fundamental proof of the particle nature of light and a high-yield topic for JEE Main. A quick shortcut for competitive exams is using the formula \( E(\text{in eV}) \approx \frac{1240}{\lambda(\text{in nm})} \). However, when specific values of \(h\) and \(e\) are provided in the question, always use them to ensure absolute precision.
To build a stronger foundation in quantum mechanics, threshold frequency, and stopping potential, refer to our comprehensive notes on the Structure of Atom Class 11 Chemistry.
Explore More Chemistry Resources
- Access full-length chapter summaries, NCERT solutions, and practice quizzes for Class XI Chemistry.
- Aiming for top ranks? Strengthen your concepts with our expert-crafted materials for Class XII Chemistry.
No comments:
Post a Comment