The velocity of electron ejected from platinum surface is $$6.54$$×$$10xm/s$$ when radiation of $$200$$ nm falls on it. Work function of platinum is $$5eV.1eV=1.6$$×$$10$$−$$19J$$. The value of x $$is__$$

Question

The velocity of electron ejected from platinum surface is $$6.54$$×$$10xm/s$$ when radiation of $$200$$ nm falls on it. Work function of platinum is $$5eV.1eV=1.6$$×$$10$$−$$19J$$. The value of x $$is__$$

Infinity Learn · Accepted Answer

Using Einstein's photoelectric equation:

$\begin{array}{l} E_{i} = K E + ϕ \\ K E = E_{i} - ϕ \\ 1 / 2 {mV}^{2} = h v - h v_{0} \\ h v = 1 / 2 {mV}^{2} + h v_{o} \end{array}$

E_i: energy of incident radiation; KE: kinetic energy of electron, and $ϕ$ : work function of metal

$\begin{matrix} E_{i} = h \frac{c}{λ} \\ = \frac{(6.63 \times 10^{- 34}) \times (3 \times 10^{8})}{200 \times 10^{- 9}} = 9.945 \times 10^{- 19} J \end{matrix}$

$\begin{array}{l} ϕ = 5 eV = 5 \times (1.6 \times 10^{- 19}) J = 8.0 \times 10^{- 19} J \\ \Rightarrow E_{k} = E_{i} - ϕ = 9.945 \times 10^{- 19} - 8.0 \times 10^{- 19} \\ Now E_{k} = 1 / 2 m v^{2} \Rightarrow v = \sqrt{\frac{2 E_{k}}{m}} \end{array}$

$\Rightarrow v = \sqrt{\frac{2 (1.195 \times 10^{- 19})}{(9.1 \times 10^{- 31})}} = 6.54 \times 10^{5} m / s$

Electromagnetic radiation and spectra

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The velocity of electron ejected from platinum surface is $6.54 \times 10^{x}$ m/s when radiation of 200 nm falls on it. Work function of platinum is $5 eV . (1 eV = 1.6 \times 10^{- 19} J)$ . The value of x is__

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Electromagnetic radiation and spectra

Unlock the full solution & master the concept.

The velocity of electron ejected from platinum surface is 6.54×10xm/s when radiation of 200 nm falls on it. Work function of platinum is 5eV.1eV=1.6×10−19J. The value of x is__

Ready to Test Your Skills?

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The velocity of electron ejected from platinum surface is $6.54 \times 10^{x}$ m/s when radiation of 200 nm falls on it. Work function of platinum is $5 eV . (1 eV = 1.6 \times 10^{- 19} J)$ . The value of x is__