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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: answer × 1 0 20 \text{answer}\times10^{20}

Detains and assumptions:

  • Threshold frequency: The minimum frequencyof radiation below which no photoelectric emission takes place is called threshold frequenc( δ 0 \delta_0 ).

  • Take the Planck's constant = 6.625 × 1 0 34 m 2 k g / s =6.625\times10^{-34}m^2kg/s and velocity of light = 3 × 1 0 8 m / s =3\times10^8m/s .

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The answer is 6.26.

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1 solution

Sravanth C.
Sep 29, 2015

We have Threshold wavelength λ 0 = 680 × 1 0 9 m \lambda_0=680×10^{-9}m , and wavelength of incident radiation λ = 560 × 1 0 9 m \lambda=560×10^{-9}m By Einstein's equation we know that, E = W + T m a x T m a x = E W E=W+T_{max}\\ T_{max}=E-W

Where E E is the energy of the incident photon, W W is the photoelectric work function and T m a x T_{max} is the maximum kinettic energy. But we also have E = h δ = c λ E=h\delta=\dfrac c\lambda and W = h δ 0 = c λ 0 W=h\delta_0=\dfrac c{\lambda_0} .

Hence the equation becomes, T m a x = h c λ h c λ 0 = h c ( 1 λ 1 λ 0 ) = 6.625 × 1 0 34 × 3 × 1 0 8 ( 1 560 × 1 0 9 1 680 × 1 0 9 ) T m a x = 6.26 × 1 0 20 J T_{max}=\dfrac{hc}\lambda-\dfrac{hc}{\lambda_0}\\=hc\left(\dfrac 1\lambda-\dfrac 1{\lambda_0}\right)\\=6.625×10^{-34}×3×10^8\left(\dfrac 1{560×10^{-9}}-\dfrac 1{680×10^{-9}}\right)\\T_{max}=\boxed{6.26×10^{-20}J}

And the solution is 6.26 × 10 20 × 1 0 20 = 6.26 6.26×10{-20}×10^{20}=\boxed{6.26}

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