Question

Albert Einstein proposed a radically new picture of electromagnetic radiation to explain photoelectric effect.

1. Identify Einstein’s photoelectric equation ?

2. With the help of Einstein’s photoelectric equation explain the following facts.

• Kinetic energy of photo electrons is directly proportional to frequency not on intensity. 
• Existence of threshold frequency for a given photosensitive material.

3. A metal whose work function is 2 eV is illuminated by light of wavelength 3 × 10^-7 m. Calculate

• threshold frequency
• maximum energy of photo electrons
• the stopping potential.

Answer 1

1. hν = hν₀ + 1/2 mv² 

2. Einstein’s photoelectric equation:

a.  hν ∝ 1/2 mv²

1/2 mv² ∝ ν

Hence kinetic energy is proportional to frequency.

b. hν – hν₀ = 1/2 mv² 

h(ν – ν₀) = 1/2 mv²

ν should be greater than ν₀ other wise h(ν – ν₀) is negative and is not possible.

3. Φ₀ =hv₀ - 2ev

v = \(\frac{c}{v}=\frac{3\times10^8}{3\times10^{-7}}\) = 10¹⁵Hz

a.  Φ₀ = hν₀

ν₀ = \(\frac{2\times1.6\times10^{-19}}{6.63\times10^{-34}}\)

= 4.8 × 10¹⁴ Hz 

b. 1/2 mv² = h(ν – ν₀)

= 6.63 × 10^-34(10¹⁵ – 4.8 × 10¹⁴)

= 3.44 × 10^-19J

c.  ev₀ = h(ν – ν₀)

= V₀ = \(\frac {h(v-v_0)}{e}\)

 = \(\frac{3.44\times10^{-19}}{1.6\times10^{-19}}\) = 5.746 V