Question

A star which can be seen with **** eye from Earth has intensity 1.6 × 10–9 Wm–2 on Earth. If the corresponding wavelength is 560 nm, and the radius of the human eye is 2.5 × 10–3 m, the number of photons entering in our in 1 is………

(A) 7.8 × 104 *–1

(B) 8.85 × 104 *–1

(C) 7.85 × 105 *–1

(D) 8.85 × 105 *–1

Answer 1

*The correct option is (B) 8.85 × 104 –1.**

Explanation:

I = intensity = 1.6 × 10–9 W/m2

λ = 560 nm = 560 × 10–9 m

r = 2.5 × 10–3 m

t = 1 sec

Intensity = {(Energy) / (area × time)} = {(power) / (area)} = (P/A)

∴ P = power = IA

Also P = {nhc / λ}

Hence {nhc / λ} = IA

∴ n = {(IAλ) / hc}

∴ n = [{1.6 × 10–9 × π × (2.5 × 10–3)2 × 560 × 10–9} / {6.63 × 10–34 × 3 × 108}]

= 884.06 × {(10–24) / (10–26)}

= 8.85 × 102 × 102

= 8.85 × 104 per second