The maximum wavelength of a beam of light that can be used to produce photo electric effect on a metal is 250 nm. The energy of the electrons in Joule, emitted from the surface of the metal when a beam of light of wavelength 200 nm is used [h = 6.62×10-34 Js, C = 3 × 108 ms-1]

The energy of the electrons emitted from the surface of the metal when a beam of light of wavelength 200 nm is used is:

19.86 × 10^-20 J

Detailed Calculation:

1. Maximum wavelength allowed for photoelectric effect: λ_max = 250 nm
2. Threshold frequency (ν₀): 
   Using the formula: 
   ν₀ = c / λ_max
   Substitute the given values: 
   c = 3 × 10⁸ m/s, λ_max = 250 nm = 250 × 10^-9 m 
   ν₀ = (3 × 10⁸) / (250 × 10^-9) 
   ν₀ = 1.2 × 10¹⁵ Hz
3. Threshold energy (Work function): 
   Using the formula: 
   E₀ = h × ν₀
   Substitute the given values: 
   h = 6.62 × 10^-34 J·s, ν₀ = 1.2 × 10¹⁵ Hz 
   E₀ = (6.62 × 10^-34) × (1.2 × 10¹⁵) 
   E₀ = 7.944 × 10^-19 J
4. Energy of incident light: 
   Using the formula: 
   E = h × c / λ
   Substitute the given values: 
   λ = 200 nm = 200 × 10^-9 m 
   E = (6.62 × 10^-34) × (3 × 10⁸) / (200 × 10^-9) 
   E = (6.62 × 3) × 10^-19 / 200 
   E = 9.93 × 10^-19 J
5. Kinetic energy of emitted electrons: 
   Using the formula: 
   KE = E - E₀
   Substitute the values: 
   KE = (9.93 × 10^-19) - (7.944 × 10^-19) 
   KE = 1.986 × 10^-19 J 
   KE = 19.86 × 10^-20 J

Concept:

• The photoelectric effect depends on the energy of incident light.
• If the light energy exceeds the threshold energy, electrons are emitted.
• Kinetic energy of electrons = Energy of incident light - Threshold energy.
• Planck's constant (h) and the speed of light (c) are used to calculate photon energy.