Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ___

Q: Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ____. (Given: h = 6.63 x 10-34 J.s and c = 3 x 108 m/s)

where: P = Power of the laser n = number of photons emitted per second h = Planck's constant c = speed of light lambda = wavelength P = 6 mW = 6 x 10-3 J/s lambda = 663 nm = 663 x 10-9 m h = 6.63 x 10-34 J.s c = 3 x 108 m/s Notice that 6.63 / 663 = 10-2. Always look for complementary numerical values like 663 and 6.63. It guarantees a clean power of 10 extraction. Class 12 Physics: Dual Nature of Radiation and Matter

Year	2026	2025	2024	Total
Questions	7	16	8	31

Year

2026

2025

2024

Total

Questions

Solution & Explanation

Related Formula

P = n (hc)/(λ)

where: $P$ $P$ = Power of the laser $n$ $n$ = number of photons emitted per second $h$ $h$ = Planck's constant $c$ $c$ = speed of light $λ$ $\lambda$ = wavelength

Step 1: Extract Given Variables

$P = 6 mW = 6 \times 10⁻³ J/s$ $λ = 663 nm = 663 \times 10⁻⁹ m$ $h = 6.63 \times 10⁻³⁴ J.s$ $h = 6.63 \times 10^{-34} \text{ J.s}$ $c = 3 \times 10⁸ m/s$ $c = 3 \times 10^8 \text{ m/s}$

Step 2: Substitution and Calculation

6 \times 10⁻³ = n \times 6.63 \times 10⁻³⁴ \times 3 \times 10⁸663 \times 10⁻⁹

Notice that $6.63 / 663 = 10⁻²$ $6.63 / 663 = 10^{-2}$.

6 \times 10⁻³ = n \times 3 \times 10⁻²⁶ \times 10⁻²10⁻⁹

6 \times 10⁻³ = n \times 3 \times 10⁻¹⁹

n = 6 \times 10⁻³3 \times 10⁻¹⁹ = 2 \times 10¹⁶

Pattern Recognition

Always look for complementary numerical values like $663$ $663$ and $6.63$ $6.63$. It guarantees a clean power of 10 extraction.

Chapter Mix

Class 12 Physics: Dual Nature of Radiation and Matter

More Dual Nature of Radiation and Matter Previous-Year Questions — Page 7

Q50 jee_main_2024_31_jan_morning Photoelectric Effect

When a metal surface is illuminated by light of wavelength

λ

, the stopping potential is

8 V

. When the same surface is illuminated by light of wavelength

3λ

, stopping potential is

2 V

. The threshold wavelength for this surface is:

A. $5λ$ $5\lambda$
B. $3λ$ $3\lambda$
C. $9λ$ $9\lambda$
D. $4.5λ$ $4.5\lambda$

Solution

Related Formula

(hc)/(λ) = φ + Kmax

Kmax = eV₀

φ = (hc)/(λ₀)

Core Logic

Using Einstein's Photoelectric equation for the two cases:

Case 1 (Wavelength $λ$ $\lambda$, Stopping Potential $8 V$ $8\mathrm{\,V}$):

(hc)/(λ) = (hc)/(λ₀) + 8e (i)

Case 2 (Wavelength $3λ$ $3\lambda$, Stopping Potential $2 V$ $2\mathrm{\,V}$):

(hc)/(3λ) = (hc)/(λ₀) + 2e (ii)

Step 2: Solving the Equations

Multiply equation (ii) by 4 to eliminate $e$ $e$:

(4hc)/(3λ) = (4hc)/(λ₀) + 8e

Equating this to equation (i):

(hc)/(λ) - (hc)/(λ₀) = (4hc)/(3λ) - (4hc)/(λ₀)

Divide entirely by $hc$ $hc$:

(1)/(λ) - (1)/(λ₀) = (4)/(3λ) - (4)/(λ₀)

(4)/(λ₀) - (1)/(λ₀) = (4)/(3λ) - (1)/(λ)

(3)/(λ₀) = (4 - 3)/(3λ)

(3)/(λ₀) = (1)/(3λ)

λ₀ = 9λ

Chapter Mix

Class 12 Physics: Dual Nature Of Radiation And Matter

Number of photons of equal energy emitted per second by a $6 mW$ $6 \text{ mW}$ laser source operating at $663 nm$ $663 \text{ nm}$ is ____. (Given: $h = 6.63 \times 10⁻³⁴ J.s$ $h = 6.63 \times 10^{-34} \text{ J.s}$ and $c = 3 \times 10⁸ m/s$ $c = 3 \times 10^{8} \text{ m/s}$)

Solution & Explanation

Related Formula

Step 1: Extract Given Variables

Step 2: Substitution and Calculation

Pattern Recognition

Chapter Mix

Reference Study Guides

More Dual Nature of Radiation and Matter Previous-Year Questions — Page 7

Solution

Related Formula

Core Logic

Step 2: Solving the Equations

Chapter Mix

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Number of photons of equal energy emitted per second by a 6 mW$6 \text{ mW}$ laser source operating at 663 nm$663 \text{ nm}$ is ____. (Given: h = 6.63 × 10⁻³⁴ J.s$h = 6.63 \times 10^{-34} \text{ J.s}$ and c = 3 × 10⁸ m/s$c = 3 \times 10^{8} \text{ m/s}$)

Solution & Explanation

Related Formula

Step 1: Extract Given Variables

Step 2: Substitution and Calculation

Pattern Recognition

Chapter Mix

Reference Study Guides

More Dual Nature of Radiation and Matter Previous-Year Questions — Page 7

Solution

Related Formula

Core Logic

Step 2: Solving the Equations

Chapter Mix

More Dual Nature of Radiation and Matter Questions — jee_main_2026_28_january_evening

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Number of photons of equal energy emitted per second by a $6 mW$ $6 \text{ mW}$ laser source operating at $663 nm$ $663 \text{ nm}$ is ____. (Given: $h = 6.63 \times 10⁻³⁴ J.s$ $h = 6.63 \times 10^{-34} \text{ J.s}$ and $c = 3 \times 10⁸ m/s$ $c = 3 \times 10^{8} \text{ m/s}$)