The threshold wavelength for a metal is 680 nanometers. Find the maximum kinetic energy of photoelectrons emitted, when a radiation of wavelength 560 nanometers is incident on the metal.
Provide the answer as:
Detains and assumptions:
Threshold frequency: The minimum frequencyof radiation below which no photoelectric emission takes place is called threshold frequenc( ).
Take the Planck's constant and velocity of light .
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We have Threshold wavelength λ 0 = 6 8 0 × 1 0 − 9 m , and wavelength of incident radiation λ = 5 6 0 × 1 0 − 9 m By Einstein's equation we know that, E = W + T m a x T m a x = E − W
Where E is the energy of the incident photon, W is the photoelectric work function and T m a x is the maximum kinettic energy. But we also have E = h δ = λ c and W = h δ 0 = λ 0 c .
Hence the equation becomes, T m a x = λ h c − λ 0 h c = h c ( λ 1 − λ 0 1 ) = 6 . 6 2 5 × 1 0 − 3 4 × 3 × 1 0 8 ( 5 6 0 × 1 0 − 9 1 − 6 8 0 × 1 0 − 9 1 ) T m a x = 6 . 2 6 × 1 0 − 2 0 J
And the solution is 6 . 2 6 × 1 0 − 2 0 × 1 0 2 0 = 6 . 2 6