Determine the longest wavelength of light required to remove an electron from a sample of potassium metal, if the binding energy for an electron in k is 1,76x10*3 kj/mol.

The wavelength of light is 68 nm.

Explanation:

Given data:

Binding energy of electron = 176 × 10³ Kj/ mol or   (1.76× 10⁶ j/mol)

Wavelength of light require to remove the  electron = ?

Solution:

E = hc / λ

h = planck constant (6.63×10⁻³⁴ J/s)

c = speed of light = (3×10⁸ m/s)

The energy require per electron is

1.76 × 10⁶ j / 6.02× 10²³ = 2.92 × 10⁻¹⁸ J

Now we will put the values in formula,

E = hc / λ

λ =  hc / E

λ = 6.63×10⁻³⁴ m².kg.s⁻¹ . 3×10⁸ m/s / 2.92 × 10⁻¹⁸ J

λ = 19.89×10⁻²⁶ m /2.92 × 10⁻¹⁸   (m².kg.s⁻² = J)

λ = 6.8 ×10⁻⁸ m

λ = 6.8 ×10⁻⁸ × 10⁹

λ = 68 nm

The energy require per electron is

Now we will put the values in formula,

E = hc / λ

λ =  hc / E  

Thus, the longest wavelength is 68nm.

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