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zhannawk [14.2K]
3 years ago
6

The work function for metallic potassium is 2.3 eV. Calculate the velocity in km/s for electrons ejected from a metallic potassi

um surface by light of wavelength 260 nm.
Chemistry
1 answer:
mote1985 [20]3 years ago
5 0

Answer:

932.44 km/s

Explanation:

Given that:

The work function of the magnesium = 2.3 eV

Energy in eV can be converted to energy in J as:

1 eV = 1.6022 × 10⁻¹⁹ J

So, work function = 2.3\times 1.6022\times 10^{-19}\ J=3.68506\times 10^{-19}\ J

Using the equation for photoelectric effect as:

E=\psi _0+\frac {1}{2}\times m\times v^2

Also, E=\frac {h\times c}{\lambda}

Applying the equation as:

\frac {h\times c}{\lambda}=\psi _0+\frac {1}{2}\times m\times v^2

Where,  

h is Plank's constant having value 6.626\times 10^{-34}\ Js

c is the speed of light having value 3\times 10^8\ m/s

m is the mass of electron having value 9.11\times 10^{-31}\ kg

\lambda is the wavelength of the light being bombarded

\psi _0=Work\ function

v is the velocity of electron

Given, \lambda=260\ nm=260\times 10^{-9}\ m

Thus, applying values as:

\frac{6.626\times 10^{-34}\times 3\times 10^8}{260\times 10^{-9}}=3.68506\times 10^{-19}+\frac{1}{2}\times 9.11\times 10^{-31}\times v^2

3.68506\times \:10^{-19}+\frac{1}{2}\times \:9.11\times \:10^{-31}v^2=\frac{6.626\times \:10^{-34}\times \:3\times \:10^8}{260\times \:10^{-9}}

\frac{1}{2}\times 9.11\times 10^{-31}\times v^2=7.64538\times 10^{-19}-3.68506\times 10^{-19}

\frac{1}{2}\times 9.11\times 10^{-31}\times v^2=3.96032462\times 10^{-19}

v^2=0.869446\times 10^{12}

v = 9.3244 × 10⁵ m/s

Also, 1 m = 0.001 km

<u>So, v = 932.44 km/s</u>

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