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Chapter 18: Q1TY (page 460)

What is the wavelength, wavenumber, and name of radiation with an energy of 100 kJ/mol?

Short Answer

Expert verified

The wavelength is1.20μm

The wavenumber is0.83μm-1

The name of radiation is Infrared radiation.

Step by step solution

01

Expression:

The expression for energy is E=hcλ

Rewrite the expression forλ:

λ=hcE

The expression for wavenumber isrole="math" localid="1663647990022" ν¯=1λ

02

Calculate wavelength:

Consider

h=6.626×10-34J⋅sc=2.998×108m/sE=100kJ/mol

Substitute in equation for wavelength,

λ=hcE

λ=6.626×10-34J⋅s)(2.998×108m/s)(6.626×1023molecules/mol100kJ/mol(103J)1kJ

≈(1.20×10-6m)106μm1m=1.20μm

The wavelength is 1.20μm

03

Calculate wavenumber:

ν¯=1λ

Substitute λ=1.20μm,

ν¯=11.20μm≈0.83μm-1

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