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Volgvan
3 years ago
5

The energy of a photon needed to cause ejection of an electron from a photoemissive metal is expressed as the sum of the binding

energy of the electron plus the kinetic energy of the emitted electron. When photons of 4.00×10-7 m light strike a calcium metal surface, electrons are ejected with a kinetic energy of 6.26×10-20 J. a Calculate the binding energy of the calcium electrons.
Chemistry
1 answer:
slega [8]3 years ago
5 0

Answer:

Binding\ energy=43.43\times 10^{-20}\ J

Explanation:

Using the expression for the photoelectric effect as:

E=h\nu_0+\frac {1}{2}\times m\times v^2

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

\nu_0=\frac {c}{\lambda_0}

Applying the equation as:

\frac {h\times c}{\lambda}=\frac {hc}{\lambda_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

\lambda is the wavelength of the light being bombarded

Given, \lambda=4.00\times 10^{-7}\ m

\frac {hc}{\lambda_0} is the binding energy or threshold energy

\frac {1}{2}\times m\times v^2 is the kinetic energy of the electron emitted.  = 6.26\times 10^{-20}\ J

Thus, applying values as:

\frac{h\times c}{\lambda}=Binding\ Energy+Kinetic\ Energy

\frac{6.626\times 10^{-34}\times 3\times 10^8}{4.00\times 10^{-7}}\ J=Binding\ Energy+6.26\times 10^{-20}\ J

\frac{19.878}{10^{19}\times \:4}\ J=Binding\ Energy+6.26\times 10^{-20}\ J

49.69\times 10^{-20}\ J=Binding\ Energy+6.26\times 10^{-20}\ J

Binding\ energy=43.43\times 10^{-20}\ J

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