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Question
When electromagnetic radiation of wavelength 300nm falls on the surface of sodium, electrons are emitted with a kinetic energy of 1.68 x 105. What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted?
When electromagnetic radiation of wavelength 300nm falls on the surface of sodium, electrons are emitted with a kinetic energy of 1.68 x 105. What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted?
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Solution
Dear student!
From photoelectric effect , we can calculate the energy of one photon as:
E =hv = hc/λ
Putting the values we get,
E = (6.62 x 10-34 Js x 3 x 108 m/s )/ 300 x 10 -9 m = 6.62 x 10-19 J
So, the energy for one mole of photons =6.62 x 10-19 x 6.022x 1023 = 3.99 x 105 J
Sinc, kinetic energy of electrons = 1.68 x 10 5J
So, minimum energy required to remove 1mole of electrons from sodium = (3.99 x 105 )- (1.68 x 105) = 2.31 x 105 J
Hence, minimum energy required to remove one electron = 2.31 x 105/ 6.022x 1023 =3.84 x 10-19 J
Now, wavelength , λ = hc/E = (6.62 x 10-34 Js x 3 x 108 m/s )/ 3.84 x 10-19 J = 5.17 x 10-7 m = 517 nm
From photoelectric effect , we can calculate the energy of one photon as:
E =hv = hc/λ
Putting the values we get,
E = (6.62 x 10-34 Js x 3 x 108 m/s )/ 300 x 10 -9 m = 6.62 x 10-19 J
So, the energy for one mole of photons =6.62 x 10-19 x 6.022x 1023 = 3.99 x 105 J
Sinc, kinetic energy of electrons = 1.68 x 10 5J
So, minimum energy required to remove 1mole of electrons from sodium = (3.99 x 105 )- (1.68 x 105) = 2.31 x 105 J
Hence, minimum energy required to remove one electron = 2.31 x 105/ 6.022x 1023 =3.84 x 10-19 J
Now, wavelength , λ = hc/E = (6.62 x 10-34 Js x 3 x 108 m/s )/ 3.84 x 10-19 J = 5.17 x 10-7 m = 517 nm
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