First slide

Quantum mechanical model of the atom

Question

The radiations obtained from deexcitation of H-atom from second orbit to 1st, striked on a metal of work function $ϕ$ 4.2 eV. The wavelength (in $\overset{o}{A}$ ) of ejected electron having maximum kinetic energy is:

Moderate

Solution

$\begin{aligned} E_{2 - 1} = 10 .2 eV; W = 4 .2 eV \\ E = 4 .2 + KE \\ ∴ 10 .2 = 4 .2 + KE \\ ∴ {KE}_{max} = 6 eV \\ \frac{1}{2} {mu}^{2} = KE \\ or λ = \sqrt{\frac{150}{KE}} = \sqrt{\frac{150}{6}} = 5 Å \end{aligned}$

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