JEE Main 2026 — Apr 2, Shift 1 — Physics solution

JEE Main2026Apr 2, Shift 1Physics

For a certain metal, when monochromatic light of wavelength $λ$ is incident, the stopping potential for photoelectrons is $3 V_{0}$ . When the same metal is illuminated by light of wavelength $2 λ$ , then the stopping potential becomes $V_{0}$ . The threshold wavelength for photoelectric emission for the given metal is $α λ$ . The value of $α$ is _____.

A
$1$
B
$4$
C
$2$
D
$3$

Solution

Einstein's photoelectric equation gives the two equations:

$\frac{h c}{λ} - ϕ = 3 e V_{0} (1)$

$\frac{h c}{2 λ} - ϕ = e V_{0} (2)$

Multiply equation (2) by $3$ and subtract from (1):

$\frac{h c}{λ} - \frac{3 h c}{2 λ} + 2 ϕ = 0 \Rightarrow 2 ϕ = \frac{h c}{2 λ} \Rightarrow ϕ = \frac{h c}{4 λ}$

The threshold wavelength satisfies $\frac{h c}{λ _{0}} = ϕ$ , hence $λ_{0} = 4 λ$ and $α = 4$ .

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