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For a certain metal, when monochromatic light of wavelength λ is incident, the stopping potential for photoelectrons is 3V₀. When the same metal is illuminated by light of wavelength 2λ, the stopping potential becomes V₀. The threshold wavelength for photoelectric emission for the given metal is αλ. The value of α is ______

Asked in JEE Main 2nd April 1st Shift 2026 · Stopping potential from wavelength

Answer: (2) 4

Step-by-step solution

Given: stopping potential 3V₀ at λ and V₀ at 2λ.

(hc)/λ-φ=3eV₀ and (hc)/(2λ)-φ=eV₀.

Subtracting: (hc)/λ-(hc)/(2λ)=2eV₀, so (hc)/(2λ)=2eV₀ and eV₀=(hc)/(4λ).

Then φ=(hc)/(2λ)-eV₀=(hc)/(2λ)-(hc)/(4λ)=(hc)/(4λ).

Threshold: λ₀=(hc)/φ=4λ, so α=4.

Why the other options are wrong

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