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Two identical photocathodes receive the light of frequencies f₁ and f₂ respectively. If the velocities of the photo-electrons coming out are v₁ and v₂ respectively, then

Asked in JEE Main 17th March 2nd Shift 2021 · Speed and kinetic energy of the photoelectrons

• (1) v₁-v₂=[(2h)/m(f₁-f₂)]^1/2
• (2) v₁²-v₂²=(2h)/m[f₁-f₂]
• (3) v₁+v₂=[(2h)/m(f₁+f₂)]^1/2
• (4) v₁²+v₂²=(2h)/m[f₁+f₂]

Step-by-step solution

Why the other options are wrong

• (1) comes from subtracts the velocities where the algebra subtracts their squares
• (3) comes from adds the two equations and then takes a square root, neither of which removes the work function
• (4) comes from adds the two equations, which leaves -2φ behind instead of cancelling it

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