JEE Main 2026 — Apr 2, Shift 2 — Chemistry solution

JEE Main2026Apr 2, Shift 2Chemistry

The surface of sodium metal is irradiated with radiation of wavelength $x$ nm. The kinetic energy of ejected electrons is $2.8 \times 1 0^{- 20}$ J. The work function of sodium is $2.3$ eV. The value of $x$ is _________ $\times 1 0^{2}$ nm. (Nearest integer)

(Given : $h = 6.6 \times 1 0^{- 34}$ J s; $1$ eV $= 1.60 \times 1 0^{- 19}$ J; $c = 3.0 \times 1 0^{8}$ m s $^{- 1}$ )

Your answer

Solution

Einstein's photoelectric equation: $\frac{h c}{λ} = W + KE$ .

Work function: $W = 2.3 \times 1.6 \times 1 0^{- 19} = 3.68 \times 1 0^{- 19}$ J.

Total photon energy: $W + KE = 3.68 \times 1 0^{- 19} + 0.28 \times 1 0^{- 19} = 3.96 \times 1 0^{- 19}$ J.

$λ = \frac{h c}{E} = \frac{6.6 \times 1 0 ^{- 34} \cdot 3 \times 1 0 ^{8}}{3.96 \times 1 0 ^{- 19}} = \frac{19.8 \times 1 0 ^{- 26}}{3.96 \times 1 0 ^{- 19}} = 5 \times 1 0^{- 7}$ m $= 500$ nm $= 5 \times 1 0^{2}$ nm.

$∴ x = 5$ .

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