Question

When electromagnetic radiation of wavelength 300 nm falls on the surface of sodium, electrons are emitted with a kinetic energy of 1.68 x 105 J mol-1 . What is the minimum energy needed to remove an electron from sodium? What is the maximum wavelength that will cause a photoelectron to be emitted?

Answer 1

Answer :

Given -

• λ (Wavelength) = 300 nm
• Kinetic energy = 1.68 × 10⁵ J mol^{-1}

To Find -

• Minimum energy to remove electron from sodium ?
• Maximum wavelength that will cause photoelectron to be emitted ?

Solution -

We know that, Energy = hv = hc/λ.

⇒ (6.626 × 10^{-34} × 3.0 × 10⁸)/(300 × 10^{-9})

⇒ 6.626 × 10^{-19} J

The energy of one mole photons :

⇒ 6.626 × 10^{-19} J × 6.022 × 10²³ mol^{-1}

⇒ 3.99 × 10⁵ J mol^{-1}

So, the minimum energy needed :

⇒ (3.99 - 1.68) 10⁵ J mol^{-1}

⇒ 2.31 × 10⁵ J mol^{-1}

Hence, the minimum energy needed to remove an electron from sodium : 2.31 × 10⁵ J mol^{-1}.

The minimum energy for electron :

⇒ (2.31 × 10⁵)/(6.022 × 10²³)

⇒ 3.84 × 10^{-19} J

Wavelength = λ

⇒ λ = hc/E

⇒ (6.626 × 10^{-34} × 3.0 × 10⁸)/(3.84 × 10^{-19})

⇒ 517 nm

Hence, The maximum wavelength that will cause photoelectron to be emitted : 517 nm.