Question

You are making photoelectric measurements on an electrode of an unknown metal. With zero potential difference applied by the battery, you shine various freqencies of light on the cathode. You detect a small photocurrent for light with wavelength up to 451 nm. What metal is the electrode made of

Answer 1

Since you detect a small photocurrent for light with wavelength up to 451 nm, the metal the electrode is made of is Sodium.

To solve the question, we need to know what work function is.

What is work function of a metal?

This is the minimum energy at which an electron will be emitted from the surface of a metal.

Since a small photocurrent is detected when ligh of wavelength up to 451 nm is applied with a zero potential difference applied, this is the threshold wavelength which gives the work function of the metal.

So, work function Ф = hc/λ where

• h = Planck's constant = 6.63 × 10⁻³⁴ Js,
• c = speed of light = 3 × 10⁸ m/s and
• λ = wavelength of light = 451 nm = 451 × 10⁻⁹ m

Substituting the values of the variables into the equation, we have

Ф = hc/λ

Ф = 6.63 × 10⁻³⁴ Js × 3 × 10⁸ m/s ÷ 451 × 10⁻⁹ m

Ф = 19.89 × 10⁻³⁴ × 10⁸ Jm ÷ 451 × 10⁻⁹ m

Ф = 0.0441 × 10⁻¹⁷ J

Ф = 4.41 × 10⁻¹⁹ J

Since 1 eV = 1.602 10⁻¹⁹ J,

Ф = 4.41 × 10⁻¹⁹ J × 1 eV/1.602 10⁻¹⁹ J

Ф = 2.753 eV

From tables, the metal with the work function closet to this value is Sodium.

So, the metal the electrode is made of is Sodium.

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