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Structure of Atom — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistryStructure of Atom3 Marks
Question
Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength $6800$ $\mathring{\text{A}}.$ Calculate threshold frequency ($ν_0 $) and work function ($W_0$​​​​​​​ ) of the metal.
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Answer

Threshold wavelength of radian $(\lambda_0)=6800\mathring{\text{A}}=6800\times10^{-10}\text{m}$
Threshold frequency ($v_0$​​​​​​​) of the metal
$=\frac{\text{c}}{\lambda_0}=\frac{3\times10^8\text{ms}^{-1}}{6.8\times10^{-7}\text{m}}=4.41\times10^{14}\text{s}^{-1}$
Thus, the threshold frequency ($v_0​​​​​​​$​​​​​​​) of the metal is $4.41 \times 10^{14} s^{–1}.$
Hence, work function ($W_0​​​​​​​$​​​​​​​) of the metal $= hν_0$
$= (6.626 \times 10^{–34}Js)(4.41 \times 10^{14} s^{–1})$
$= 2.922 \times 10^{–19}J$

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