A metal plate is illuminated by a monochromatic beam of light with a wavelength of 400 nm , and a negative potential of 1.1 V is required to halt the photocurrent. Determine the threshold wavelength for the metal.

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Quantrex Academy · Accepted Answer

Correct answer: B. 620 nm

According to Einstein's photoelectric equation:

E = \Phi + K_{\text\max}

The energy of the incident photon is given by:

E = \dfrac{hc}{\lambda} = \dfrac{1240 \text{ eV}\cdot\text{nm}}{400 \text{ nm}} = 3.1 \text{ eV}

The maximum kinetic energy of the photoelectrons is related to the stopping potential

V_0

as:

K_{\text\max} = eV_0 = 1.1 \text{ eV}

Substituting these values into the photoelectric equation:

\Phi = E - K_{\text\max} = 3.1 \text{ eV} - 1.1 \text{ eV} = 2.0 \text{ eV}

The threshold wavelength

\lambda_0

is given by:

\lambda_0 = \dfrac{hc}{\Phi} = \dfrac{1240 \text{ eV}\cdot\text{nm}}{2.0 \text{ eV}} = 620 \text{ nm}

A metal plate is illuminated by a monochromatic beam of light with...

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