# 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 BYJU'S Exam Prep

Updated on: September 25th, 2023

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. The photoelectron spectrum is created by analyzing the spectrum of energies that are present in the electrons produced when an intense photon of radiation strikes a molecule.

## Maximum Wavelength that will cause a Photoelectron to be Emitted

The question states 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? A type of energy known as electromagnetic radiation spreads as electrical and magnetic waves that move in units of energy known as photons. Electromagnetic radiation has a spectrum with varied wavelengths and frequencies, which in turn imparts various properties.

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. Excitation and ionization are the two kinds of energy that electromagnetic radiation deposits as it travels through biological material. A higher electron shell can be reached by an electron without being ejected, and this process is known as excitation.

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