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 maximum wavelength that will cause a photoelectron to be emitted?

By Ritesh|Updated : November 14th, 2022

(a) λ = 320 nm

(b) λ = 449.7 nm

(c) λ = 526 nm

(d) λ = 518 nm

The maximum wavelength that will cause a photoelectron to be emitted is 518 nm. In the photoelectric effect, light is incident on a metal surface, which causes electrons to be expelled from its surface. Photoelectrons are the name given to these expelled electrons.

We know that:

Energy of 300 nm photon = hv = hc/λ

Substituting the values we get:

= (6.626 x 10-34 Js x 3 x 108 m/s)/ 300 x 10-9 m

In simplification we get the:

= 6.626 x 10-19 J

Energy of one mole of photon = 6.626 x 10-19 J x 6.022 x 1023 mol-1

= 3.99 x 105 J mol-1

The energy of photons - Kinetic energy of electrons is the minimal energy required to remove a mole of electrons from sodium.

Substituting the values we get:

= (3.99 - 1.68) x 105 J mol-1

= 2.31 x 105 J mol-1

Minimum energy for one electron = 2.31 x 105 J mol-1/ 6.022 x 1023 mol-1

= 3.84 x 10-19 J

λ = hc/E

Substituting the values we get:

= (6.626 x 10-34 J s x 3 x 108 m/s)/ 3.84 x 10-19 J

In simplification we get the:

= 5.176 x 10-7 m

= 5.18 x 10-7 m

= 518 nm

Summary:

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 maximum wavelength that will cause a photoelectron to be emitted?

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. The maximum wavelength that will cause a photoelectron to be emitted is 518 nm.

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